my statistics exam 2

1) X ∼ N(15,5) X ∼ N (15,5), what is the P( X>1 1) P ( X > 11)? 0.7881 If X ∼ N(15,5) X ∼ N (15,5), what is the P(X<11) P ( X <11)? 0.2119 2) Suppose it is known that 10% of adolescent females in the United States have iron deficiency. In a random sample of 35 adolescent females, what is the probability that exactly 3 have iron deficiency? 84 3) A Gallup poll asked the question “If you won 10 million dollars in the lottery would you continue to work, or would you stop working?” Of the 30 randomly selected employed adults in the study, 59% said they would continue working. 90% confidence level (0.442, 0.738) 4) Construct a 95% confidence interval for the proportion of employed adults who would continue to work if they won 10 million dollars in the lottery. (0.414, 0.766) 5) An online retailer claims 90% of all orders are shipped within 12 hours of being received. Let p^ p ^be the sample proportion of orders that are shipped within 12 hours in a SRS of orders. Suppose we set our sample size to n=120 n =120 What is the probability of selecting an SRS in which less than 105 orders were shipped within 12 hours? 0.1807 An online retailer claims 90% of all orders are shipped within 12 hours of being received. Let p^ p ^ be the sample proportion of orders that are shipped within 12 hours in a SRS of orders. In a sample of size n=200 n =200, which value would be the first quartile of all sample proportions 0.8857 6) The mean amount of money spent on health insurance per month by US citizens is strongly right skewed with a mean of $456 and standard deviation of $53. Suppose a SRS of 50 US citizens is taken. Find the probability that the sample mean amount of money spent on health insurance is less than $430/month. 0.0003 7) with larger sample sizes there is a greater likelihood that the data distribution... Will look similar to the population distribution. 8) The time that it takes a randomly selected rat of a certain subspecies to find its way through a maze is normally distributed with mean μ=1.5 μ =1.5 minutes and σ=0.35 σ =0.35 minutes. Suppose 4 rats are selected. What is the probability that the sample mean time to navigate the maze is more than 1.92 minutes? 0.0082 9) An insurance company knows that in the entire population of millions of insured workers, the distribution of annual cost of workers’ compensation claims is right skewed with a mean $439 per insured worked and standard deviation $20,000. Suppose a sample of 20 workers’ compensation claim costs is taken. What is the probability that the sample mean cost is greater than $1500? This probability cannot be calculated because we do not know the sampling distribution of xˉ 10) Viral hepatitis occurs in 7% of patients who receive multiple blood transfusions during heart surgery. A SRS was taken of 200 heart surgery patients who had multiple blood transfusions. If appropriate, use the normal approximation to the binomial to find the probability that at least 10 contracted viral hepatitis. 0.8662 11)Suppose that 11% of adolescent females in the United States have iron deficiency. In a random sample of 300 adolescent females in the United States, what is the probability less than 8% of the females in the sample have iron deficiency? 0.0484 12) Which of the following statements about the t t distribution is/are true?The t t distribution is used in confidence intervals for a population mean when σ σ is estimated with s s .As the sample size increases, the t t distribution gets closer to a standard normal distribution.There t t distribution is the same regardless of the sample size. 1&2 only

13) The army reports that the distribution of head circumference among male soldiers is approximately normal with μ=22.8 inches and σ=1.1 inches. The army plans to make helmets in advance to fit the middle 98% of head circumferences for male soldiers. Soldiers who fall outside this range will get custom-fitted helmets. What head circumferences will not require custom fitted helmets? (20.24, 25.36) 14) The 2018 General Social Survey asked, “What do you think is the ideal number of children for a family to have?” From a sample of 1357 people, the mean was 2.61 with a standard deviation of 0.94. A 90% confidence interval for the true mean number of children people think a family should have is (2.568, 2.652). What is the width for this confidence interval?0.10 0.084 15) Suppose that across all departments at a large university with over 500 faculty, 25% are female. A SRS of 10 faculty members is selected and the total number of females is counted (out of the 10). Does this constitute a binomial experiment? Yes, all the conditions are met. 16) An online retailer claims 90% of all orders are shipped within 12 hours of being received. Let p^ p^ be the sample proportion of orders that are shipped within 12 hours in a SRS of orders. What is the minimum sample size required for p^ p ^to be approximately normally distributed? 100 17) Four of the 20 students (20%) in a class are fraternity or sorority members. A random sample of 5 students in the class is taken and the number of students in the sample who are fraternity or sorority members is counted (out of the 5). Does this constitute a binomial experiment? No, the probability of success is not constant from trial to trial. 18) A wildlife biologist wants to determine the mean weight of adult red squirrels. She captures 10 squirrels she believes to be representative of the species and weighs them, finding a mean of 12.32 grams and standard deviation of 1.88gm. Assuming these squirrels can be considered a random sample of all red squirrels, which of the following formulas gives a 95% confidence interval for the mean weight of all squirrels? 12.32±2.262(1.88/ root 10) 19) An actuary is interested in estimating the proportion of young adults who plan to have children someday. She takes a SRS of 60 young adults and finds that 48 of them plan to have children. Construct a 95% confidence interval for the proportion of young adults who plan to have children someday. (0.699, 0.901) 20 ) The accuracy of the Normal approximation to the binomial improves when: the number of observations, n n , increases. 21) Suppose that 11% of adolescent females in the United States have iron deficiency. In a random sample of 300 adolescent females in the United States, what is the probability more than 8% of the females in the sample have iron deficiency? 0.9516 22) Arsenic is a compound naturally occurring in very low concentrations. Arsenic blood concentrations in healthy individuals are normally distributed with a mean of 3.2 mg/dl and standard deviation of 1.5 mg/dl. Determine the required sample size to construct a 95% confidence interval to within +/- 0.5 mg/dl of the population mean. 36 21) Suppose X ∼ N (73,3) X ∼ N (73,3). What is P(67<X<73) P (67< X <73)? 0.4772 22) Which of the following will reduce the margin of error in a confidence interval? All the other answers are correct 23) An article described a study of a random sample of young adults with pierced tongues. The researchers found receding gums, which can lead to tooth loss, in 34.6% of the participants. They constructed the following 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums: (0.217,0.475)(0.217,0.475) What was the margin of error for their confidence interval? 0.129 24) Which of the following statements about the t t distribution is/are true?

46) Each of the 110 students in a statistics class selects a different random sample of 35 quiz scores from a population of 5000 scores they are given. Using their data, each student constructs a 90% confidence interval for μ μ , the average quiz score of the 5000 students. Which of the following conclusions is correct? About 90% of the confidence intervals will contain μ μ 47) Getting an adequate amount of sleep can improve a variety of physiological functions, and it is known that the average number of hours that people sleep each night is Normally distributed. A psychiatrist at a major research center takes an SRS of 25 emotionally disturbed patients and records the average amount of sleep that each gets on a typical night Suppose a 90% confidence interval for the mean amount of time that emotionally disturbed patients sleep during a typical night is (6.6,7.2)(6.6,7.2) Interpret this interval in the context of the problem We are 90% confident that the mean hours of sleep that emotionally disturbed patients get on a typical night is in this interval. 50) The accuracy of the Normal approximation to the binomial improves when: the number of observations, n n , increases. 51) An actuary is interested in estimating the proportion of young adults who plan to have children someday. She takes a SRS of 60 young adults and finds that 48 of them plan to have children. Construct a 90% confidence interval for the proportion of young adults who plan to have children someday. (0.715, 0.885) 52) In a random sample of size 10, we have a mean of 23 and a standard deviation of 4. Assuming the conditions are met, what is a 95% confidence interval for the population mean? (20.14, 25.86) 53) Four of the 20 students (20%) in a class are fraternity or sorority members. A random sample of 5 students in the class is taken and the number of students in the sample who are fraternity or sorority members is counted (out of the 5). Does this constitute a binomial experiment? Incorrect answer: No, the probability of success is not constant from trial to trial. 54) An online retailer claims 90% of all orders are shipped within 12 hours of being received. Let p^ p ^ be the sample proportion of orders that are shipped within 12 hours in a SRS of orders. What is the minimum sample size required for p^ p ^ to be approximately normally distributed? 100 55) Suppose that across all departments at a large university with over 500 faculty, 25% are female. A SRS of 10 faculty members is selected and the total number of females is counted (out of the 10). Does this constitute a binomial experiment? Yes, all the conditions are met. 56) Which of the following statements about the t t distribution is/are true? 1&2 57 )Suppose that 11% of adolescent females in the United States have iron deficiency. In a random sample of 300 adolescent females in the United States, what is the probability less than 8% of the females in the sample have iron deficiency? 0.0484 58) Viral hepatitis occurs in 7% of patients who receive multiple blood transfusions during heart surgery. A SRS was taken of 200 heart surgery patients who had multiple blood transfusions. If appropriate, use the normal approximation to the binomial to find the probability that at least 10 contracted viral hepatitis. 0.8662 59 ) An insurance company knows that in the entire population of millions of insured workers, the distribution of annual cost of workers’ compensation claims is right skewed with a mean $439 per insured worked and standard deviation $20,000. Suppose a sample of 20 workers’ compensation claim costs is taken. What is the probability that the sample mean cost is greater than $1500? This probability cannot be calculated because we do not know the sampling distribution of xˉ 60) The time that it takes a randomly selected rat of a certain subspecies to find its way through a maze is normally distributed with mean μ=1.5 μ =1.5 minutes and σ=0.35 σ =0.35

minutes. Suppose 4 rats are selected. What is the probability that the sample mean time to navigate the maze is more than 1.92 minutes? 0.0082 61 )With larger sample sizes there is a greater likelihood that the data distribution… will look similar to the population distribution. 62)The mean amount of money spent on health insurance per month by US citizens is strongly right skewed with a mean of $456 and standard deviation of $53. Suppose a SRS of 50 US citizens is taken. Find the probability that the sample mean amount of money spent on health insurance is less than $430/month. 0.0003 62) An online retailer claims 90% of all orders are shipped within 12 hours of being received. Let p^ p ^be the sample proportion of orders that are shipped within 12 hours in a SRS of orders. Suppose we set our sample size to n=120 n =12. What is the probability of selecting an SRS in which less than 105 orders were shipped within 12 hours? 0.1807 63) Suppose it is known that 10% of adolescent females in the United States have iron deficiency. In a random sample of 35 adolescent females, what is the probability that exactly 3 have iron deficiency? 0.225 64) The confidence level C C of a confidence interval is the probability that the confidence interval method works to capture the true value of the parameter of interest. 65) An online retailer claims 90% of all orders are shipped within 12 hours of being received. Let \hat{p} p ^ be the sample proportion of orders that are shipped within 12 hours in a SRS of orders. What is the minimum sample size required for \hat{p} p ^ to be approximately normally distributed? 66) The weight of a particular variety of watermelon is known to be Normally distributed with mean 14.2 and standard deviation 0.66. What is the probability a randomly selected watermelon weighs between 14 and 15 pounds? 0.5063 67) The development of viral hepatitis subsequent to blood transfusion can cause serious complications for a patient. This occurs in 7% of patients who receive multiple blood transfusions during heart surgery. A SRS was taken of 33 heart surgery patients who had multiple blood transfusions. Find the probability that at least 2 contracted viral hepatitis. 0.6823 The development of viral hepatitis subsequent to blood transfusion can cause serious complications for a patient. This occurs in 7% of patients who receive multiple blood transfusions during heart surgery. A SRS was taken of 33 heart surgery patients who had multiple blood transfusions. Find the probability that more than 2 contracted viral hepatitis. 0.4095 70) The proportion of baby boys born in the United States is equal to 0.512. The two histograms below represent repeated samples of newborn babies in the United States. What is the best explanation the difference in the spread of the distributions? Different sample sizes are being used. 71) According to the CDC National Center for Health Statistics, about 42.4% of adult Americans fit the medical definition of being obese. How large would a sample from this population need to be to ensure that the distribution of the sample proportion is approximately Normal? 24 72) A neurologist randomly samples 400 adult men in the United States and finds that 29 of them have experienced at least one migraine headache. Construct a 99% confidence interval for the proportion of adult men in the United States who have experienced at least one migraine headache. (0.039, 0.106) 73) In the US, we categorize adolescent girls as either anemic, border line anemic or as having a normal level of iron in their blood. Suppose 10% of adolescent girls are anemic, 15% are border line anemic and the rest have normal iron levels in their

Between 87 and 103 A cookie company has decided to sell its cookies in packages that are advertised to contain “less than 100 calories.” In truth, the calorie count per package is normally distributed with mean 95 and standard deviation 4. What is the probability that a randomly selected package of cookies will have a calorie count more than 105? 0.0062 84) The juror pool for an upcoming trial contains the names of 1,000 people who may be called for jury duty. The proportion of potential jurors who are Hispanic or Latinx is 0.40. A jury of size 12 is randomly selected. Let X X = the number of people on the jury who are Hispanic or Latinx. Is this a binomial setting? Yes, all the conditions are met. 85) Suppose 10% of all purchasers of a refrigerator buy an extended warranty. In a random sample of 20 refrigerator purchasers, let X X represent the sample count who buy an extended warranty. What is the probability that X X is less than 2 0.3917 86) Suppose a 95% confidence interval for p p is (0.487, 0.663). Which of the following interpretations is correct? Out of 100 intervals, approximately 95 will contain the true proportion p p and 5 will not. 87) Which of the following are true of p^ p ^ is a statistic p ^ is a categorical random variable p ^ describes categorical data 1 and 3 only 87) Suppose a botanist grows many individually potted eggplants, all treated identically and arranged in groups of 4 pots on the greenhouse bench. After 30 days of growth, she measures the Which of the following is a true statement about the sampling distribution for the average leaf area of each group of 4 plants? 88) The lengths of herring (a type of fish) are normally distributed with μ=54 μ =54 mm and σ=4 σ =4mm. What length of fish is longer than 73.89% of the fish in the population? 56.56 mm 89) 56.56 mm 90) Suppose you are planning an experiment in which you are going to take a SRS of 236 cars and measure their O2 emission levels. As part of your report, you decide to give a 95% confidence interval for μ μ = average emission level. If instead, you decreased your confidence level to 90%, what would be the impact on your estimation of the parameter μ μ ? The chance you will select a sample whose calculated confidence interval would not contain the true value of μ μ will double. 91) One hundred rats whose mothers were exposed to high levels of tobacco smoke during pregnancy were put through a simple maze. The maze required the rats to make a choice between going left or right at the outset. Out of the 100 rats sampled, 80 went right when running the maze for the first time. Assume that the 100 rats can be considered an SRS from the population all rats born to mothers exposed to high levels of tobacco smoke during pregnancy. Let p p be the proportion of rats in this population that would go right when running the maze for the first time. A 90% confidence interval for p is: 0.734, 0.866) 92) The distribution of the average number of hours college students spend sleeping each weeknight is strongly right skewed with a mean of 5 and a standard deviation of 1. If we were to imagine taking all possible samples of size 15 from the population of college students, what would the shape of the sampling distribution of the sample means be? Less skewed than the population 93)

The 2018 General Social Survey asked, “What do you think is the ideal number of children for a family to have?” From a sample of 1357 people, the mean was 2.61 with a standard deviation of 0.94. A 94% confidence interval for the true mean number of children people think a family should have is (2.568, 2.652). What is the margin of error for this confidence interval? 0.042 93) The distribution of textbook sales for all college students is right skewed with a mean of $200 and a standard deviation of $120. Suppose that a researcher who didn’t know this information sampled 40 students. She found that the students paid $180 on average with a standard deviation equal to $109. What is the data distribution? 94) Suppose X ∼ N(73,3) X ∼ N (73,3). Between which two values would the middle 95% of all X X values fall? (67.12, 78.88) 95) Suppose that 11% of adolescent females in the United States have iron deficiency. Let p^ be the sample proportion of females that have iron deficiency in a SRS of females in the Unites States. What is the minimum sample size required for p^ p ^to be approximately normall7 distributed? 91 96) As part of a promotion for a new type of cracker, free trial samples are offered to shoppers in a local supermarket. The probability that a shopper will buy a packet of crackers after tasting the free sample is 0.2. Different shoppers can be regarded as independent trials. Use the normal approximation to the binomial to calculate the probability that at least 28 of the next 100 shoppers who sample the crackers will buy a pack. 0.0228 97) Which of the following is true of p^? P^ is a quantitative random variable 98) A recent poll indicates that 48% of all registered voters in America plan to vote for a specific candidate in the upcoming presidential election. If a random sample of 15 voters is taken, what is the probability that less than 2 of them plan to vote for the candidate? 0.0008 100) Consider a sample of tissue cells infected in a laboratory treatment. For 225 tissues, the mean was 350 and the standard deviation was 80 for the number of cells infected. The standard error is: 5.333 101) A presidential candidate urged voters to complete an online public opinion survey. Of the approximately 1.4 million respondents, 98% agreed with the candidate's health care reform platform. Are the assumptions met for computing a confidence interval for the proportion of all voters who agree with the candidate's health care reform platform? No, because the data are from a voluntary response sample. 102) Suppose 2% of American females aged 15-19 are pregnant. In a random sample of 50 females between the ages of 15 and 19, what is the probability that exactly 1 is pregnant? 0.3716 103) Suppose 2% of American females aged 15-19 are pregnant. In a random sample of 50 females between the ages of 15 and 19, what is the probability that 1 or fewer are pregnant? 0.7358 104) Let X X be the cholesterol level of a randomly chosen individual. Assume that cholesterol levels are normally distributed with mean μ μ = 203 and standard deviation σ σ = 20. Let xˉ x ˉbe the sample mean cholesterol level of a randomly chosen sample of 10 individuals. Between which two values would the middle 90% of sample means fall? Between 192.6 and 213.4 105) Suppose X ∼ N X ∼ N (23,4)(23,4). Between which two numbers would the middle 92%of all X X values fall?

115) The mean amount of money spent on health insurance per month by US citizens is strongly right skewed with a mean of $456 and standard deviation of $53. Suppose a SRS of 50 US citizens is taken. Find the probability that the sample mean amount of money spent on health insurance is less than $430/month. 0.0003 116) Suppose a researcher is interested in determining the average length of gestation among pregnant Canadian women. Gestation length is approximately Normally distributed. He takes a SRS of 36 Canadian women who have given birth within the last year and calculates the length of gestation in days for each of them, getting a sample mean of 272.25 and a standard deviation of 14.25. (269.148, 275.352) 117) Body temperature in humans is normally distributed with mean 98.2° F and standard deviation 0.5° F. What body temperature is lower than 97.5% of all other body temperatures? 97.22° F 118) An actuary is interested in estimating the proportion of young adults who plan to have children someday. She takes a SRS of 60 young adults and finds that 48 of them plan to have children. Construct an 80% confidence interval for the proportion of young adults who plan to have children someday. (0.734, 0.866) 119) Suppose that for people in Idaho the population mean number of hours worked per week is 40.2 hrs and the population standard deviation is 0.4 hrs. 95% of all sample means from all possible samples of size 40 will fall between which two values? (40.08,40.32) 120) Suppose 10% of all purchasers of a refrigerator buy an extended warranty. Use the normal approximation to the binomial to calculate the probability that less than 12 refrigerator purchasers in a SRS of 100 would buy an extended warranty. What is the result? 0.7475 121) The mean amount of money spent on health insurance per month by US citizens is strongly right skewed with a mean of $456 and standard deviation of $53. Suppose a SRS of 16 US citizens is taken. Find the probability that the sample mean amount of money spent on health insurance is less than $430/month. This probability cannot be calculated because we do not know the distribution of xˉ . 122) Suppose you are planning an experiment in which you are going to take a SRS of 236 cars and measure their O2 emission levels. As part of your report, you decide to give a 95% confidence interval for μ μ = average emission level. If instead, you decreased your confidence level to 90%, what would be the impact on your estimation of the parameter μ μ ? The chance you will select a sample whose calculated confidence interval would not contain the true value of μ μ will double. 123) Which of the following is NOT true about a sample proportion calculated from a sample of size n n ? It always falls within three standard deviations of the true proportion p p . 124) In a SRS of 25 men, the mean systolic blood pressure is 123.5 and the standard deviation is 9. (121.128, 125.872) 125) The National AIDS Behavioral Surveys randomly sampled 1000 adult heterosexuals and gave each a survey regarding their sexual practices. The study found that 64 of the participants had multiple partners. (0.046, 0.082) 126) Each of the 110 students in a statistics class selects a different random sample of 35 quiz scores from a population of 5000 scores they are given. Using their data, each student constructs a 90% confidence interval for μ μ , the average quiz score of the 5000 students. Which of the following conclusions is correct? About 90% of the confidence intervals will contain μ μ 127) The length of human pregnancies from conception to birth varies according to a distribution with mean 266 days and standard deviation 16 days. Suppose a random sample of 40 pregnant women is taken. Which sample mean would be the 85 th percentile of all sample mean pregnancy lengths? 268.62

128) If the height of 20-year-old American women is normally distributed with a mean of 64 inches and standard deviation of 3 inches, then the sampling distribution for the average height of 36 randomly chosen women will be: 129) Why do we need a normal population distribution or large sample size to make inference about Μ μ ? 130) Suppose that a pre-election poll of 500 people showed that 51% of the sample supported the incumbent senator. If the population proportion who supported the incumbent senator is really 48%, how likely is it that we would see poll results such as this or higher? 131) Suppose that 70% of Americans support the death penalty for persons convicted of murder. Let p hat be the sample proportion of people who support the death penalty in an SRS of Americans. The distribution of p hat will be approximately Normally distributed if the sample size is at least 34. 132) A pollster took a random sample of 100 students from a large university and computed a confidence interval to estimate the percentage of students who were planning to vote in the upcoming election. The pollster felt that the confidence interval was too wide to provide a precise estimate of the population parameter. What could the pollster have done to produce a narrower confidence interval? Increase the sample size to 200. 133) Suppose that you are a writer for a university newspaper and due to time constraints you conduct a survey of only 20 randomly selected students. You ask them, “Do you plan to watch the homecoming parade?” and 19 of them say they plan to watch. Create a 95% confidence interval for the proportion of students that plan on watching the parade. The conditions are not met to construct this interval. 134. Suppose that in a department at Southern Methodist University with 20 faculty members, 25% are female. A SRS of 5 faculty members is selected and the total number of females is counted (out of the 10). Does this constitute a binomial experiment? No, the probability of success is not constant from trial to trial 135. A couple decides that they will keep having children until they have a boy. Successive births are independent of each other and the probability of having a boy is approximately 0.50. Is this a binomial setting? No, there is not a fixed number of observations. 136. We take a random sample of 100 soda bottles and find a sample mean of 296ml. The 95% confidence interval for the true mean volume of all bottles is (294ml, 298ml). According to the manufacturer, the bottles are supposed to have an average volume of 300ml. We claim the true mean is between 294ml and 298ml. 137. Suppose you want to estimate the proportion of employed adults who would continue working if they won 10 million dollars in the lottery. A previous study on the issue had a sample proportion of 0.59. How many employed adults should be randomly sampled in order to get a 99% confidence interval with a width of 0.3? 72 138. Suppose Coke bottles have volumes which are normally distributed with mean 298ml and standard deviation 3ml. If we take a random sample of size n=9 n =9 what is the probability the sample mean volume is greater than 299ml? 0.1587 139. Suppose 2% of American females aged 15-19 are pregnant, and a random sample of 100 American females aged 15-19 is taken. Would it be appropriate to use the normal approximation to the binomial to calculate the probability that 8 or fewer are pregnant? No, because the sample size condition is not met. 140. Suppose that in the population of all university faculty members in the United States, 25% are female. A SRS of 20 university faculty members is selected and the total number of females is counted (out of the 20). Does this constitute a binomial experiment?

14.745 154. xSuppose a 70% confidence interval for p is (0.746, 0.854). Which of the following interpretations is/are correct? Suppose a 70% confidence interval for P is (0.746, 0.854). Which of the following interpretations is/are correct? Out of 100 intervals, approximately 70 will contain p^ and 30 will not. We are 70% confident that p is in this interval. There is a 70% chance that p is in this interval. All of the other statements are true. We are 70% confident that p is in this interval. And out of 100 intervals, approx 70 will contain p and 30 will not 155. suppose 15% of adult Americans think that “marijuana should remain illegal even for medical purposes.” Let X X represent the number of people in a SRS of 500 adult Americans who agree that “marijuana should remain illegal even for medical purposes.” What is the distribution of X? X ∼ B (500,0.15) 156. Suppose a researcher is interested in determining the average length of gestation among pregnant Canadian women. Gestation length is approximately Normally distributed. He takes a SRS of 36 Canadian women who have given birth within the last year and calculates the length of gestation in days for each of them, getting a sample mean of 272.25 and a standard deviation of 14.25. How many pregnant Canadian women should be sampled in order to get a 95% confidence interval with a width of 4.8? 142 157. Suppose that ACT scores are Normally distributed with μ=20 μ =20 and σ=5 σ =5 . Let X be the ACT score of a randomly selected student. What is P(19<X<28) P (19< X <28)? 0.5245 158. If the circumference for women’s heads is normally distributed with μ=22.2 μ =22.2 and σ=1.4 σ =1.4 inches, what proportion of women can use the ready-made helmets that exist for men? Ready-made helmets range from 20.24 to 25.36 inches in circumference. 0.9072 159. The distribution of housing prices is strongly right skewed with mean $189.2 (in thousands) and standard deviation $45 (in thousands). An SRS of 20 houses is taken. What is the probability that the mean housing price is greater than $200 (in thousands)? This probability cannot be calculated because the sampling distribution of x is unknown. 160. The average number of acres burned by wildfires in the United States is 780 acres with standard deviation 500 acres. Since some wildfires burn thousands of acres, the distribution of acres burned by wildfires is strongly right skewed. Suppose a SRS of 100 wildfires is taken. Find the probability that the sample mean number of acres burned is greater than 830 acres. 0.1586 161. An actuary is interested in estimating the proportion of young adults who plan to have children someday. She takes a SRS of 60 young adults and finds that 48 of them plan to have children. Construct an 80% confidence interval for the proportion of young adults who plan to have children someday. (0.734, 0.866) 162. Suppose a 95% confidence interval for p is (0.487, 0.663). Which of the following interpretations is correct? Out of 100 intervals, approximately 95 will contain the true proportion p and 5 will not. 163. As part of a promotion for a new type of cracker, free trial samples are offered to shoppers in a local supermarket. The probability that a shopper will buy a packet of crackers after tasting the free sample is 0.2. Different shoppers can be regarded as independent trials. If X is the number among the next 100 shoppers who buy a packet of crackers after tasting a free sample, then the distribution of X is approximately: N (20,4) 164. A certain population is strongly skewed to the right. We want to estimate its mean, so we will collect a sample. Which should be true if we use a large sample rather than a small one? 1. The data distribution of our sample will be closer to normal. 2. The sampling distribution of the sample means will be closer to normal.

3. The variability of the sampling means will be greater. 2 only 165. In the US, 35% of teenagers have severe acne. Use the Normal approximation to the binomial to calculate the chance that less than 30 teenagers in an SRS of 100 would have severe acne. 0.1473 166. Suppose you want to estimate the mean number of children desired by adults over the age of 25. A previous study on this issue had a sample standard deviation of 1.81. How many adults should be randomly sampled in order to get a 95% confidence interval with a margin of error of ±0.25±0.25? 210 167. Consider a sample of tissue cells infected in a laboratory treatment. For 225 tissues, the mean was 350 and the standard deviation was 80 for the number of cells infected. The standard error is: 5.333 168. Which of the following is true of ^ p p ^ is a quantitative random variable 169. A cookie company has decided to sell its cookies in packages that are advertised to contain “less than 100 calories.” In truth, the calorie count per package is normally distributed with mean 95 and standard deviation 4. Between which two numbers would the middle 92% of all calorie counts per package fall? Between 88.00 and 102.00 170. The length of human pregnancies from conception to birth varies according to a distribution with mean 266 days and standard deviation 16 days. Suppose a random sample of 40 pregnant women is taken. Which sample mean would be the 15 th percentile of all sample mean pregnancy lengths? 263.37 171. The weight of a particular variety of watermelon is known to be Normally distributed with mean 14.2 and standard deviation 0.66. What is the probability a randomly selected watermelon weighs between 13 and 15 pounds? 0.8527 172. Suppose X ∼ N(23,4)(23,4). Between which two numbers would the middle 94% of all X values fall? Between 15.48 and 30.52 173. A statistics professor asked her students whether or not they were registered to vote. In a sample of 50 of her students (randomly sampled from her 700 students), 35 said they were registered to vote. She used this data to construct a 95% confidence interval for the true proportion p of all her students who were registered to vote. This confidence interval either captured the true proportion p p , or it didn't. There is no probability involved. 174. Let X be the resting heart rate of a physically fit man. Assume that the resting heart rate for fit men follows a Normal distribution with mean μ = 60 and standard deviation σ σ = 10. Let x be the sample mean resting heart rate for a randomly chosen sample of 35 fit men. What value is the 95 th percentile of all sample mean resting heart rates? 175. Which of the following will reduce the width of a confidence interval, thereby making it more informative? Increasing the sample size

187. In a SRS of 25 men, the mean systolic blood pressure is 123.5 and the standard deviation is 9. Construct a 90% confidence interval for the mean systolic blood pressure of men. (120.420, 126.580) 188. Suppose that the mean household income in the United States is $55,000 with a standard deviation of $20,000. A SRS of 30 individuals in taken. Find the probability that the mean household income for these people is greater than $60,000. 0.0855 189. The life spans of a species of fruit fly are normally distributed with a mean of 36 days and a standard deviation of 4 days. What fruit fly life span is longer than 80% of all other fruit fly life spans? 39.37 1,3 only 191. A neurologist randomly samples 400 adult men in the United States and finds that 29 of them have experienced at least one migraine headache. How many adult men in the United States should be sampled in order to get a 90% confidence interval with a width of 0.03? 809 192. Suppose that in a population of voters in Dallas, TX, 38% are in favor of a particular bond issue. A random sample of 900 voters is taken, and 360 are in favor of the bond issue. What is the sampling distribution of the sample proportion in this scenario? 193. The National AIDS Behavioral Surveys randomly sampled 1000 adult heterosexuals and gave each a survey regarding their sexual practices. The study found that 64 of the participants had multiple partners. Which of the following interpretations of the interval from the previous problem is/are correct? Out of 100 intervals, approximately 98 will contain the true proportion of adults heterosexulas with multiple partners and approximately 2 of them will not Suppose a 95% confidence interval for the mean daily sales for a sample of 100 days from an internet site is ($236,$318)($236,$318) . If the sample size were decreased to 50 days, the resulting 95% confidence interval would be: Wider Suppose it is known that 5% of men aged 50 and older have prostate cancer. In a random sample of 25 men aged 50 and older, what is the probability that exactly 2 have prostate cancer? 0.2305 Which of the following statements is true about the Central Limit Theorem? It requires randomly gathered data and a large enough sample size n

According to the CDC National Center for Health Statistics, about 42.4% of adult Americans fit the medical definition of being obese. Suppose we set our sample size to be n n = 200. What is the probability of choosing a SRS of American adults in which more than 45% of them are obese? 0.2284 A candidate for public office is believed to have the support of 60% of voters. Assume the number of voters is in the millions. An SRS of 5 voters is selected and the total number of people who support the candidate are counted (out of the 5). What is the probability that less than 3 support the candidate? 0.3174 Getting an adequate amount of sleep can improve a variety of physiological functions, and it is known that the average number of hours that people sleep each night is normally distributed. A psychiatrist at a major research center takes an SRS of 25 emotionally disturbed patients and records the average amount of sleep that each gets on a typical night. He summarizes the data and finds that \bar{x}=6.90 x ˉ=6.90 and s=0.878 s =0.878. Construct a 95% confidence interval for the mean amount of time that emotionally disturbed patients sleep during a typical night. (6.54, 7.26) Suppose that 40% of Saguaro cacti have owls nesting in them. Let \hat{p} p ^ be the sample proportion of cacti that have owls nesting in them in a SRS of n=30 n =30 Saguaro cacti. What is the probability of choosing a SRS in which less than 45% of the cacti have owls nesting in them? 0.7119 Viral hepatitis occurs in 7% of patients who receive multiple blood transfusions during heart surgery. A SRS was taken of 200 heart surgery patients who had multiple blood transfusions. If appropriate, use the Normal a pproximation to the binomial to find the probability that less than 10 contracted viral hepatitis. 0.1388 The margin of error of a confidence interval estimates the error… caused by using a sample rather than the whole population. Scientists discovered a new group of proteins in an animal species. They found that the distribution of the number of amino acids these proteins were made of was approximately normal with mean 530 and standard deviation 80. According to the Empirical Rule, about what percent of these new proteins will be more than 690 amino acids long? 2.5%