Answer Key for Week 6 Assignment – Part 1 Utica College – MAT112 D. Higgins This answer key was adapted from OpenStax Statistics, Instructor Answer and Solution Guide, Chapter 7: The Central Limit Theorem. Exercise 61. Previously, De Anza statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a mean of $0.88. Suppose that we randomly pick 25 daytime statistics students. a. In words, Χ= ____________ b. Χ~ _____(_____,_____) c. In words, ࠵?= ____________ d. ࠵?~ ______ (______, ______) e. Find the probability that an individual had between $0.80 and $1.00. Graph the situation, and shade in the area to be determined. f. Find the probability that the average of the 25 students was between $0.80 and $1.00. Graph the situation, and shade in the area to be determined. g. Explain why there is a difference in part e and part f. Exercise 63. According to the Internal Revenue Service, the average length of time for an individual to complete (keep records for, learn, prepare, copy, assemble, and send) IRS Form 1040 is 10.53 hours (without any attached schedules). The distribution is unknown. Let us assume that the standard deviation is two hours. Suppose we randomly sample 36 taxpayers. a. In words, Χ= _____________ b. In words, ࠵?= _____________ c. ࠵?~ _____(_____,_____) d. Would you be surprised if the 36 taxpayers finished their Form 1040s in an average of more than 12 hours? Explain why or why not in complete sentences. e. Would you be surprised if one taxpayer finished his or her Form 1040 in more than 12 hours? In a complete sentence, explain why.
Answer Key for Week 6 Assignment – Part 1 Utica College – MAT112 D. Higgins c. d. Yes. I would be surprised, because the probability is almost 0. e. No. I would not be totally surprised because the probability is 0.2312 Exercise 65. The length of songs in a collector’s iTunes album collection is uniformly distributed from two to 3.5 minutes. Suppose we randomly pick five albums from the collection. There are a total of 43 songs on the five albums. a. In words, Χ= _________ b. Χ~ _____________ c. In words, ࠵?= _____________