The customer care manager at a cell phone company

1. The customer care manager at a cell phone company keeps track of how long each help-line
caller spends on hold before speaking to a customer service representative. He finds that the
distribution of wait times for all callers has a mean of 12 minutes with a standard deviation of
5 minutes. The distribution is moderately skewed to the right. Suppose the manager takes a
random sample of 10 callers and calculates their mean wait time, .
(a) What is the mean of the sampling distribution of ?
(b) Is it possible to calculate the standard deviation of ? x If it is, do the calculation. If it isn’t,
explain why.
(c) Do you know the approximate shape of the sampling distribution of ? x If so, describe the
shape and justify your answer. If not, explain why not.
x
x

316 The Practice of Statistics, 4/e- Chapter 7 © 2011 BFW Publishers
2. The weights of Granny Smith apples from a large orchard are Normally distributed with a
mean of 380 gm and a standard deviation of 28 gm.
(a) A single apple is selected at random from this orchard. What is the probability that it
weighs more 400 gm?
(b) Three apples are selected at random from this orchard. What is the probability that their
mean weight is greater than 400 gm.?
(c) Explain why the probabilities in (a) and (b) are not equal.

© 2011 BFW Publishers The Practice of Statistics, 4/e- Chapter 7 317
Quiz 7.3B AP Statistics Name:
1. The service department of a large automobile dealership keeps records of the odometer
readings of cars that it repairs and determines that the distribution of miles driven per year by
all of its customers has a mean of 14,000 miles and a standard deviation of 4000. The
distribution is skewed to the right. Suppose a random sample of 12 cars is taken from the
hundreds of cars for which they have records, and mean number of miles per year, , x is
calculated.
(a) What is the mean of the sampling distribution of ?
(b) Is it possible to calculate the standard deviation of ? x If it is, do the calculation. If it
isn’t, explain why.
(c) Do you know the approximate shape of the sampling distribution of ? x If so, describe
the shape and justify your answer. If not, explain why not.
x

318 The Practice of Statistics, 4/e- Chapter 7 © 2011 BFW Publishers
2. The weights of newborn children in the United States vary according to the Normal
distribution with mean 7.5 pounds and standard deviation 1.25 pounds. The government
classifies a newborn as having low birth weight if the weight is less than 5.5 pounds.
(a) What is the probability that a baby chosen at random weighs less than 5.5 pounds at birth?
(b) You choose three babies at random and compute their mean weight, x . What is the
probability that their average birth weight is less than 5.5 pounds?
(c) Explain why the probabilities in (a) and (b) are not equal.

© 2011 BFW Publishers The Practice of Statistics, 4/e- Chapter 7 319
Quiz 7.3C AP Statistics Name: