summer13test1

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Dixie State University *

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2040

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Statistics

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Jan 9, 2024

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docx

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4

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STAT2040 Name: __________________________________ SUMMER 2013 MID-TERM I Please write your name on the exam before moving on. Read each problem before attempting it. The specific language is critical. Use any method discussed in class to solve the problems. When using Excel © be sure to include inputs. If you get stuck on the calculation problems - make assumption and continue - partial credit is available. Failure to show your method of solution could result in loss of points even for a correct answer. 100 pts possible --------------------------------------------------------------------------------------------------------------------- Multiple Choice (3 pts. Each) 1. Approximately what percentage of scores falls within two standard deviation of the mean in a normal distribution? a. 34% b. 95% c. 99% d. 68% 2. If the population distribution is unknown, how large must the sample size be to assume the sample is normally distributed? a. 10 b. 25 c. 30 d. 100 e. 200 3. The ______ is the value you calculate when you want the arithmetic average. a. Mean b. Median c. Mode d. All of the above 4. The _______ is often the preferred measure of central tendency if the data are severely skewed. a. Mean b. Median c. Mode d. Range 5. Fill in the missing words to the quote: “Inferential statistics may be described as methods for drawing conclusions about _________ based on computed _________from a ________ .” (A) statistics, samples, populations (B) populations, parameters, samples (C) statistics, parameters, samples (D) parameters, statistics, populations (E) populations, statistics, sample Page 1
6. If a test was generally very hard, except for a few students who had very high scores, then the distribution of scores would be _____. a. Positively skewed b. Negatively skewed c. Not skewed at all d. Normal 7. How many ways can an IRS auditor select 4 of 10 tax returns for an audit (hint: order does not matter)? a. 5040 b. 40 c. 2.5 d. 210 e. Not enough information is given. 8. Of 1100 people who came into a blood bank to give blood, 350 had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure. a. 50% b. 82% c. 32% d. <0001% e. 100% 9. The weighted average of possible returns, with the weights being the probabilities of occurrence is referred to as __________. a. a probability distribution b. the expected return c. the standard deviation d. coefficient of variation 10. A method of using samples to estimate population parameters is known as: a. statistical interference. b. statistical inference. c. statistical variance 11. The lower case Greek letter m or represents the population __________ in statistics equations. a. Mean b. Mode c. Variance d. Standard Deviation e. Sum Page 2
12. (Descriptive Statistics – 10 pts) Ten men in two age groups were randomly sampled. Calculate the mean, median and standard deviation of the Body Mass Index (BMI) for each group. How do the two groups differ in central tendency and distribution? (One or two sentences or bullet points is sufficient.) Men ages 20-29 Men ages 40+ Mean Median Standard Deviation 13. (Conditional Probability – 10 pts) A study of on-time flight service was conducted with the following results. Skywish airline had 33 on-time flights and 6 late flights. CanyonAir had 43 on-time flights and 5 late flights. If one flight is randomly selected, find the probability that the flight was a CanyonAir flight given that it was late. Skywish CanyonAir On-time Late 14. (Probability – 10) A class has 5 students who are to be assigned seating by using a random drawing. What is the probability that the students will be arranged in order from oldest to youngest (assume that no two students are exactly the same age). Page 3 Answer:
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15. (Expected Value – 10 pts) Rainfall in St. George tends to be variable. Given the following annual rain totals and probabilities, calculate the expected rainfall for an average year. Rain (inches) Probability ---------------------------------------------- 10 .05 4 .25 8 .60 2 .10 16. (Normal Distributions – 10 pts) Give that Women’s heights are normally distributed with mean 63.6 in. and standard deviation 2.5 in. You want a mail order bride to be between 60 and 66 inches. What percentage of the population are you potentially eliminating from your pool of candidates? 17. (Descriptive Statistics – 10 pts) There are three positive integers a,b, and c, where c is larger than b, and b is larger than a. The median, mean, and range of the three are 11, 9, and 10, respectively. Find a. 18. (Probability – 10 pts) - You have a bag of marbles with 7 red marbles, 4 blue marbles, 5 purple marbles, 3 pink marbles, 9 white marbles, 16 black marbles, and 1 green marble. You randomly pick one marble from the bag. What is the probability it is not blue? What is the probability it is not blue, given that you know it isn’t black? Extra Credit (5pts) Three ants are at the three corners of a triangle - one ant per corner. If all three start walking to another corner, what is the probability none will collide? Page 4