According to a report, smartphone owners on average use 21 apps per month with a standard deviation of 4 apps. The probability questions ask for the likelihood that random samples of 25 or 144 smartphone owners have a mean app usage between 20-21.5. With a larger sample of 144, the standard error is smaller so the sampling distribution is more concentrated, increasing the probability of the sample mean being close to the population mean of 21.

1. According to a report from a business intelligence company, smartphone owners are using an
average of 21 apps per month. Assume that number of apps used per month by smartphone
owners is normally distributed and that the standard deviation is 4 . Complete parts (a) through (d)
below. a. If you select a random sample of 25 smartphone owners, what is the probability that the
sample mean is between 20.5 and 21.5 ? (Round to three decimal places as needed.) b. If you
select a random sample of 25 smartphone owners, what is the probability that the sample mean is
between 20 and 21 ? (Round to three decimal places as needed.) c. If you select a random
sample of 144 smartphone owners, what is the probability that the sample mean is between 20.5
and 21.5 ? (Round to three decimal places as needed.) 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 (1) than in (a). As the
standard error (2) values become more concentrated around the mean. Therefore, the probability
that the sample mean will fall close to the population mean will always (3) when the sample size
increases. (1) less (2) increases, (3) increase greater decreases, decrease