PSTAT 5A
Unit 5 Practice Problems
1. The waiting time (in minutes) of 15 calls to a customer service hotline are as
follows: 10, 1, 2, 9, 5, 3, 4, 1, 0, 5, 6, 5, 3, 9, 3
A. Calculate the mean and standard deviation.
B. Find the 5-number summary.
C. Construct a box-plot of the data.
D. What is a more useful measurement of “center” for the data: mean,
median, or mode? Why?
2. The mean height of American men (ages 20 – 29) has a distribution with
mean 69.2 inches and standard deviation 2.9 inches. A random sample of 60
such men are selected.
A. Define the random variable of interest.
B. Find the mean and standard deviation of the sampling distribution.
C. Find the probability that the mean height of the sample is greater than
71 inches.
3. A tomato variety produces fruit with weights that are normally distributed
with mean 127 grams and a standard deviation of 22 grams. Suppose that
we have 12 of these tomatoes with independent weights.
A. Find the expected value and standard deviation of the mean of these
12 tomatoes.
B. Calculate the probability that the average is greater than 125 grams.
C. Which event has a larger probability: one tomato weighs between 120
and 134 grams, or the average of 12 tomatoes is between 120 and
134 grams.
4. A survey of 700 residents of Santa Barbara asked them whether they favored
widening the 101 from two lanes to three. The survey found that 476 of
them favored the proposal.
A. Define the parameter and random variable of interest.
B. Find the expected value and standard deviation of the random
variable.
C. State the distribution of the random variable.