Question
According to a report from a business intelligence company, smartphone owners are using an average of 22 apps per month. Assume that number of apps
According to a report from a business intelligence company, smartphone owners are using an average of
22
apps per month. Assume that number of apps used per month by smartphone owners is normally distributed and that the standard deviation is
5.
Complete parts (a) through (d) below.
Question content area bottom
Part 1
a. If you select a random sample of
36
smartphone owners, what is the probability that the sample mean is between
21.5
and
22.5?
(Round to three decimal places as needed.)
Part 2
b. If you select a random sample of
36
smartphone owners, what is the probability that the sample mean is between
21
and
22?
(Round to three decimal places as needed.)
Part 3
c. If you select a random sample of
144
smartphone owners, what is the probability that the sample mean is between
21.5
and
22.5?
(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
than in (a). As the standard error
values become more concentrated around the mean. Therefore, the probability that the sample mean will fall close to the population mean will always
decrease
increase
when the sample size increases.
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