STAT Homework 7 Solution

Problem 1 (2:5 points)

An elevator can safely hold 3; 500 lbs. A sign in the elevator limits the passenger count to 15. If the adult population has a mean weight of 180 lbs with a 25 lbs standard deviation, how unusual would it be, if the central limit theorem applied, that an elevator holding 15 people would be carrying more than 3; 500 pounds? (Hint: if X is a random variable indicating a person’s weight, then assume X Normal( = 180; 2 = 252); use related d, p, q, and r functions to get the numerical answer.)

Problem 2 (2:5 points)

A restaurant sells an average of 25 bottles of wine per night, with a variance of 25. Assum-ing the central limit theorem applies, what is the probability that the restaurant will sell more than 600 bottles in the next 30 days? (Hint: if X is a random variable indicating one day sale, then assume X Poisson( = 25); use related d, p, q, and r functions to get the numerical answer.)

Problem 3 (2 points)

Currently, there are 52 enrolled students in STAT 3355. It is known that 13:1% of the population in U.S. are left-handed. A student wishes to find the proportion of left-handed people in this class. She surveys 30 students and finds that only 2 are left-handed. If she computes a 95% confidence interval, would it contain the value of 13:1%?

Problem 4 (3 points)

For the babies dataset in the package UsingR, the variable age contains the mother’s age and the variable dage contains the father’s age. Find a 95% confidence interval for the difference in mean age. Does it contain 0? What do you assume about the data?

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