# EXS_EX.2.2007Fall - SOLUTIONS MAT 167 Statistics Test II...

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SOLUTIONS MAT 167: Statistics Test II: Chapters 4-7 Instructor: Anthony Tanbakuchi Fall 2007 Name: Computer / Seat Number: No books, notes, or friends. Show your work. You may use the attached equation sheet, R, and a calculator. No other materials. If you choose to use R, copy and paste your work into a word document labeling the question number it corresponds to. When you are done with the test print out the document. Be sure to save often on a memory stick just in case. Using any other program or having any other documents open on the computer will constitute cheating. You have until the end of class to finish the exam, manage your time wisely. If something is unclear quietly come up and ask me. If the question is legitimate I will inform the whole class. Express all final answers to 3 significant digits. Probabilities should be given as a decimal number unless a percent is requested. Circle final answers, ambiguous or multiple answers will not be accepted. Show steps where appropriate. The exam consists of 4 questions for a total of 25 points on 9 pages. This Exam is being given under the guidelines of our institution’s Code of Academic Ethics . You are expected to respect those guidelines. Points Earned: out of 25 total points Exam Score:
MAT 167: Statistics, Test II: Chapters 4-7 SOLUTIONS p. 1 of 9 1. Assume that men’s waists are normally distributed with μ = 35 in and σ = 2 . 3 in. Solution: Let’s write down the given information: > mu = 35 > sigma = 2.3 (a) (1 point) If 1 man is randomly selected, find the probability that his waist size is greater than 34 in. Solution: Find P ( x > 34) using the normal distribution and the given parameters: > p = 1 - pnorm (34 , mean = mu, sd = sigma ) > s i g n i f (p , 3) [ 1 ] 0.668 (b) (1 point) If 20 men are randomly selected, find the probability that their mean waist size is less than 34 in. Solution: Find P x < 34) using the normal distribution for the sampling distribution of ¯ x (since the CLT applies). The standard deviation will be the standard error: > n = 20 > std . err = sigma/ sqrt (n) > p = pnorm (34 , mean = mu, sd = std . err ) > s i g n i f (p , 3) [ 1 ] 0.0259 (c) (1 point) You are designing sweat pants that are “one size fits all”. In reality, the pants only stretch out to fit the bottom 90% of the male waist sizes, what is the maximum waist size that the pants will stretch to? Solution: Solve for a in P ( x < a ) = 0 . 90, therefore use the inverse normal cumulative distribution using the given parameters: > a = qnorm ( 0 . 9 , mean = mu, sd = sigma ) > s i g n i f (a , 3) [ 1 ] 37.9 Instructor: Anthony Tanbakuchi Points earned: / 3 points
MAT 167: Statistics, Test II: Chapters 4-7 SOLUTIONS p. 2 of 9 2. The clothing manufacturer’s association (CMA) publishes data that manufacture’s use to de- termine what sizes of clothing they should make. As mentioned before, the CMA states that men’s waists are normally distributed with μ = 35 in and σ = 2 . 3 in. Lately, you are getting a lot of returns on your one size fit’s all sweat pants (that you designed in a previous question) because they are too small.