Bow Valley College Probabilities Statistics Questions

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Question 1. According to the Internal Revenue Service, the average length of time for an individual tocomplete (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 standarddeviation is two hours. Suppose we randomly sample 36 taxpayers.(a) Suppose ? ? =The total length of time for 36 taxpayers to complete IRS Form 1040. What is thedistribution of ? ?. (Show your calculations and formulas)(b) What is the probability that the total length of time for 36 taxpayers to complete IRS Form isbetween 380 and 385 hours? (Show your calculations, formulas and the curve)(c) What is the probability that the total length of time for 36 taxpayers to complete IRS Form ismore than 390 hours? (Show your calculations, formulas and the curve)(d) Find the 75th percentile for the total length of time for 36 taxpayers. (Show your calculations andformulas)

Question 2. Suppose that a category of world-class runners is known to run a marathon (26 miles) in anaverage of 145 minutes with a standard deviation of 14 minutes. Consider 49 of the races. Let ?% theaverage of the 49 races.(a) ?%~ _____(_____,_____). (Show your calculations and formulas)(b) Find the probability that the runner will average between 142 and 146 minutes in these 49marathons. (Show your calculations, formulas and the curve)(c) Find the 80th percentile and 25th percentile for the average of these 49 marathons. (Show yourcalculations, formulas and the curve)(d) Find the median of the average running times. (Show your calculations, formulas and the curve)

Question 3. Salaries for teachers in a particular elementary school district are normally distributed witha mean of $44,000 and a standard deviation of $6,500. We randomly survey ten teachers from thatdistrict.(a) What is the distribution of the total salaries of ten teachers? (Show your calculations andformulas)(b) Find the probability that the teachers earn a total of over $400,000. (Show your calculations,formulas and the curve)(c) Find the probability that the teachers earn a total of less than $425,000. (Show yourcalculations, formulas and the curve)(d) Find the 95th percentile for the sum of ten teachers’ salary. (Show your calculations, formulasand the curve)