According to a report from a business intelligence company, smartphone owners are using an average of

23

apps per month. Assume that number of apps used per month by smartphone owners is normally distributed and that the standard deviation is

3.

Complete parts (a) through (d) below.

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Part 1

a. If you select a random sample of

25

smartphone owners, what is the probability that the sample mean is between

22.5

and

23.5?

0.600.60

(Round to three decimal places as needed.)

Part 2

b. If you select a random sample of

25

smartphone owners, what is the probability that the sample mean is between

22

and

23?

0.45220.4522

(Round to three decimal places as needed.)

Part 3

c. If you select a random sample of

100

smartphone owners, what is the probability that the sample mean is between

22.5

and

23.5?

0.90460.9046

(Round to three decimal places as needed.)

Part 4

d. Explain the difference in the results of (a) and (c).

The sample size in (c) is greater than the sample size in (a), so the standard error of the mean (or the standard deviation of the sampling distribution) in (c) is

less

greater

than in (a). As the standard error

increases,

decreases,

values become more concentrated around the mean. Therefore, the probability that the sample mean will fall close to the population mean will always

increase

decrease

when the sample size increases.