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According to a report from a business intelligence company, smartphone owners are using an average of 17 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. a. If you select a random sample of 25 smartphone owners, what is the probability that the sample mean is between 19.5 and 20.5



Answer :

Let's simplify the problem using the standard normal distribution and the z-formula. First, we find the corresponding z-values for 19.5 and 20.5:

Z1 = 19.5-17 / 0.6 = 2.5/0.6 ≈ 4.167

Z2 = 20.5-17 / 0.6 = 3.5/0.6 ≈ 5.833

Then, we look up these z-values in a standard normal distribution table and find the corresponding probabilities. However, since these z-values are quite large, the probability that the sample mean is between 19.5 and 20.5 is practically zero.