# Sampling Distribution Homework 4

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```					                      Sampling Distribution Homework 4
Chapter 9

1. The following data represent the number of days absent per year in a population
of 6 employees of a small company:
1 3 6 7 7 12
a. compute the population mean and standard deviation
b. select all possible samples of size 2 and set up the sampling distribution of
the mean
c. compute the mean of the sample means, compute the standard error
d. select all possible samples of size 3 and set up the sampling distribution of
the mean
e. compute the mean of the sample means, compute the standard error
f. compare the shape of sampling distributions for b. and d.

2. The diameter of Ping-Pong balls manufactured at a large factory is expected to be
approximately normally distributed with a mean of 1.3 inches and a standard
deviation of .04 inches. What is the probability that a randomly selected Ping-
Pong ball will have a diameter
a. Less than 1.28 inches?
b. Between 1.28 and 1.32 inches?
c. Between what two values (symmetrically distributed around the mean)
will 60% of the Ping-Pong balls fall (in terms of diameter)?

If many random samples of 16 Ping-Pong balls are selected
d. What will be the values of the population mean and standard error of the
mean?
e. What distribution will the sample means follow?
f. What proportion of the sample means will be less than 1.28 inches?
g. What proportion of the sample means will be between 1.28 and 1.32
inches?
h. Between what two values (symmetrically distributed around the mean)
will 60% of the sample means be?
i. Which is more likely to occur – an individual ball between 1.28 and 1.32
inches or a sample mean between 1.28 and 1.32 inches? Explain.

3. A call center has a history of receiving calls that last an average of 150 seconds
with a standard deviation of 15 seconds.
a. What is the probability that a single call is between 150 and 155 seconds?
b. What is the probability that a sample of 35 calls will yield a mean between
150 and 155 seconds?

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