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 month by smartphone owners is normally...

Extracted text: 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 month by smartphone owners is normally distributed and that the standard deviation is 6. Complete parts (a) through (d) below. a. If you select a random sample of 16 smartphone owners, what is the probability that the sample mean is between 22.5 and 23.5? .259 (Round to three decimal places as needed.) b. If you select a random sample of 16 smartphone owners, what is the probability that the sample mean is between 22 and 23? 0.249 (Round to three decimal places as needed.) 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? 0.593 (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 greater than in (a). As the standard error decreases, values become more concentrated around the mean. Therefore, the probability that the sample mean wi fall close to the population mean will always increase when the sample size increases.