Description
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(µ = 180, σ2 = 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. Assuming 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(λ = 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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