1. Determine whether the statement is true or false. Write T if the statement is true and F if false. 1. The total area under the normal distribution curve is less than 1. 2. The normal distribution curve is skewed to the left. 3. The standard normal distribution has a mean of 0. 4. In a normal distribution, the mean, the median, and the mode are not equal. 5. The standard deviation of the sampling distribution of sample statistics is also called the standard error. 6. Measures computed using pon
1. Determine whether the statement is true or false. Write T if the statement is true and F if false. 1. The total area under the normal distribution curve is less than 1. 2. The normal distribution curve is skewed to the left. 3. The standard normal distribution has a mean of 0. 4. In a normal distribution, the mean, the median, and the mode are not equal. 5. The standard deviation of the sampling distribution of sample statistics is also called the standard error. 6. Measures computed using pon
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
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Transcribed Image Text:1. Determine whether the statement is true or false. Write T if the statement is true and F if false.
1. The total area under the normal distribution curve is less than 1.
2. The normal distribution curve is skewed to the left.
3. The standard normal distribution has a mean of 0.
4. In
normal distribution, the mean, the median, and the mode are not equal.
5. The standard deviation of the sampling distribution of sample statistics is also called the standard error.
6. Measures computed
using population data are called parameters.
7. The Central Limit Theorem states that the sampling distribution of the sample means approaches the t-
distribution when n is large.
8. The lesser the degrees of freedom for a t-distribution, the more the tails of the distribution are stretched.
9. The t-distribution, just like the normal distribution, is unimodal, symmetric, and bell-shaped.
10. The lower and upper limits of an interval estimate can be computed by subtracting and adding the
standard error from the point estimate.
For numbers 11-14.
Determine the area under the standard normal curve of the following graph.
-2.65
Z-1.50
26. q = ?
1.71
Z-1.50
a. 0.03%
For numbers 15-18. What is the probability of the following?
15-16. P(Z<1.75)
a. 95.99%
b. 91.98%
c. 45.99%
17-18. P(1.31<z<2.63)
a. 99.57%
b. 90.06%
c. 49.57%
For numbers 19-22. Given: μ = 30; a = 6; P(x > 20), find the following:
19-20. What is the value of z?
a. 1.67
b. 1.2
c. -1.2
d. -1.67
21-22. What is the area of the distribution?
a. 95.25%
b. 49.95%
23. Given: 90% confidence, n = 18. Find t = ?
b. 2.110
a. 2.458
11-12. Area:
13-14. Area:
b. 50%
24. What is df on the given from number 23?
a. 19
b. 18
c. 17
For numbers 25-26. Given: x = 164, n = 250, E = 2%, find the following:
25. p = ?
a.0.80%
c. 65.60%
c. 45.25%
c. 1.740
c. 34.40%
b. 3.44%
27-28. Given: p=0.55 and E=0.02, what is the value of n?
b. 1,674
a. 1,674.35
c. 2,377
d. 4.01%
d. 9.08%
d. 4.75%
d. 1.734
d. 16
d. 100%
d. 99.2%
d. 2,376.99
![For numbers 29 - 32. Athena earned a score of 750 on a national achievement test. The mean score was
625, with a standard deviation of 175. Assume that test scores are normally
distributed.
29-30. What is Athena's z-score?
a. 0.71
b. -0.71
c. 0.0.92
31-32. What is the probability of students having a higher score than Athena?
a. 23.89% of the students had a score lower than Athena.
b. 23.89% of the students had a score higher than Athena.
c. 26.11% of the students had a score higher than Mary.
d. none of the above
33-34. The weights of males are normally distributed with a mean of 190 lbs and a standard deviation of
20 lbs. What is the probability that a randomly selected male weigh more than 175 lbs?
a. The probability that a randomly selected male weigh less than 175 lbs is 77.34%
b. The probability that a randomly selected male weigh less than 175 lbs is 22.66%
The probability that a randomly selected male weighs greater than 175 lbs is 77.34%
All The probability that a randomly selected male weighs greater than 190 lbs is 22.66%
35-36. All vehicles for registration in the Philippines are required to pay the tax value. The value depends
on the model of the car. The mean and standard deviation of the tax value of Dan's car are μ =
P456,000 and a = P182,500 respectively. Suppose random samples of size 150,000 are drawn from
the population of vehicles. What is the standard error of the mean?
c. 1,177.39
a. 1,067.42
b. 706.17
C.
d. 471.21
For numbers 37-40. It is known that cellular phone batteries produced by a certain factory have lifetimes
that follow a normal distribution. The average lifetime of the batteries is known to
be 2.8 years with a standard deviation of 0.45 years. A random sample of size 16
will be taken, and the probability has a sample mean less than 3 years,
37-38. What is the z-value of 3 years?
a. - 1.78
b. 1.78
d. -0.92
C. -0.44
d. 0.44
39-40. What is the percentage that a random sample of size 16 will have a sample mean less than 3
years?
a. P(Z < 1.78) = 96.24%
b. P(Z < 0.44) = 67%
c. P(Z > -1.78) = 96.24%
d. P(z > -0.44) = 67%
For numbers 41-44. A random sample of 40 snack prices is taken from a grocery store. The mean of
the sample is 23.25, and the sample standard deviation is 4.73. Using a 95%
confidence level, answer the following:
41-42. What is the margin of error for the mean price of all candies in the grocery store?
a. 0.75
b. 1.47
c. 1.53
d. 2
43-44. Construct a 95% confidence interval for the mean price of all the candies in the grocery store.
a. [23.05, 23.44] b. [22.02, 24.48] c. [21.78, 24.72] d. [23.02, 23.48]
45-46. Ten randomly selected automobiles were stopped, and the tread depth of the right front tire was
measured. The mean was 0.23 inch, and the standard deviation was 0.06 inch. Find the 95%
confidence interval of the mean depth. Assume that the variable is approximately normally
distributed.
a. 0.19<u<0.27
b. 0.17<u<0.29
c. 0.22 μ<0.24
d. 0.21<u<0.25
47 - 48. In a survey of 1,500 Filipino adults, 375 of them said that their favorite sport to watch is football.
Construct a 90% confidence interval for the proportion of Filipino adults who say football is their
favorite sport to watch.
a. 23.1% <p<26%
c. 23.3% <p<26.7%
d. 23.2% <p<26.8%
b. 23.2%<p<26.7%
49-50. A random sample of eight high school students had the following number of absences: 10, 6, 7, 8,
5, 4, 10, and 12. Assume that the number of days of absences is normally distributed. Which of
the following is true?
a. The standard error of the estimate of absences is 2.76.
b. At 95% level of confidence, the margin of error of the estimate is 0.98.
c. The best point estimate for the true average number of days of absences is 7.75
d. The lower limit of the 95% confidence interval for the true average number of days of absences
is 7.5.
april
185](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c31935a-4721-43cc-9bc5-45074106efcc%2F8675e77e-aa84-45e3-8973-ff1993e98636%2F9kninah_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For numbers 29 - 32. Athena earned a score of 750 on a national achievement test. The mean score was
625, with a standard deviation of 175. Assume that test scores are normally
distributed.
29-30. What is Athena's z-score?
a. 0.71
b. -0.71
c. 0.0.92
31-32. What is the probability of students having a higher score than Athena?
a. 23.89% of the students had a score lower than Athena.
b. 23.89% of the students had a score higher than Athena.
c. 26.11% of the students had a score higher than Mary.
d. none of the above
33-34. The weights of males are normally distributed with a mean of 190 lbs and a standard deviation of
20 lbs. What is the probability that a randomly selected male weigh more than 175 lbs?
a. The probability that a randomly selected male weigh less than 175 lbs is 77.34%
b. The probability that a randomly selected male weigh less than 175 lbs is 22.66%
The probability that a randomly selected male weighs greater than 175 lbs is 77.34%
All The probability that a randomly selected male weighs greater than 190 lbs is 22.66%
35-36. All vehicles for registration in the Philippines are required to pay the tax value. The value depends
on the model of the car. The mean and standard deviation of the tax value of Dan's car are μ =
P456,000 and a = P182,500 respectively. Suppose random samples of size 150,000 are drawn from
the population of vehicles. What is the standard error of the mean?
c. 1,177.39
a. 1,067.42
b. 706.17
C.
d. 471.21
For numbers 37-40. It is known that cellular phone batteries produced by a certain factory have lifetimes
that follow a normal distribution. The average lifetime of the batteries is known to
be 2.8 years with a standard deviation of 0.45 years. A random sample of size 16
will be taken, and the probability has a sample mean less than 3 years,
37-38. What is the z-value of 3 years?
a. - 1.78
b. 1.78
d. -0.92
C. -0.44
d. 0.44
39-40. What is the percentage that a random sample of size 16 will have a sample mean less than 3
years?
a. P(Z < 1.78) = 96.24%
b. P(Z < 0.44) = 67%
c. P(Z > -1.78) = 96.24%
d. P(z > -0.44) = 67%
For numbers 41-44. A random sample of 40 snack prices is taken from a grocery store. The mean of
the sample is 23.25, and the sample standard deviation is 4.73. Using a 95%
confidence level, answer the following:
41-42. What is the margin of error for the mean price of all candies in the grocery store?
a. 0.75
b. 1.47
c. 1.53
d. 2
43-44. Construct a 95% confidence interval for the mean price of all the candies in the grocery store.
a. [23.05, 23.44] b. [22.02, 24.48] c. [21.78, 24.72] d. [23.02, 23.48]
45-46. Ten randomly selected automobiles were stopped, and the tread depth of the right front tire was
measured. The mean was 0.23 inch, and the standard deviation was 0.06 inch. Find the 95%
confidence interval of the mean depth. Assume that the variable is approximately normally
distributed.
a. 0.19<u<0.27
b. 0.17<u<0.29
c. 0.22 μ<0.24
d. 0.21<u<0.25
47 - 48. In a survey of 1,500 Filipino adults, 375 of them said that their favorite sport to watch is football.
Construct a 90% confidence interval for the proportion of Filipino adults who say football is their
favorite sport to watch.
a. 23.1% <p<26%
c. 23.3% <p<26.7%
d. 23.2% <p<26.8%
b. 23.2%<p<26.7%
49-50. A random sample of eight high school students had the following number of absences: 10, 6, 7, 8,
5, 4, 10, and 12. Assume that the number of days of absences is normally distributed. Which of
the following is true?
a. The standard error of the estimate of absences is 2.76.
b. At 95% level of confidence, the margin of error of the estimate is 0.98.
c. The best point estimate for the true average number of days of absences is 7.75
d. The lower limit of the 95% confidence interval for the true average number of days of absences
is 7.5.
april
185
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