Question

According to a social media blog, time spent on a certain social networking website has a mean of 22 minutes per visit.Assume that time spent on the social networking site per visit is normally distributed and that the standard deviation is 7minutes. Complete parts (a) through (d) below.a. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 21.5 and 22.5minutes?(Round to three decimal places as needed.)b. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 21 and 22minutes?(Round to three decimal places as needed.)c. If you select a random sample of 144 sessions, what is the probability that the sample mean is between 21.5 and 22.5minutes?(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 ofthe sampling distribution) in (C) is than in (a) As the standard errorvalues become moreconcentrated around the mean Therefore, the probability that the sample mean will fall in a region that includes thepopulation mean will alwayswhen the sample size increases.

Answer 1

Given:

Mean, μ = 22

Standard deviation, σ = 7

Let's answer the following questions.

a. Given:

Sample size, n = 25

Let's find the probability that the sample mean is between 21.5 and 22.5.

We have:

$\begin{gathered} P(21.5Thus, we have:[tex]\begin{gathered} P(\frac{21.5-22}{\frac{7}{\sqrt[]{25}}}Using the standard normal table (NORMSDIST), we have:[tex]\begin{gathered} P(0.3571)=0.6395 \\ P(-0.3571)\text{ = }-0.3605 \\ \\ P(1.7857)-P(-0.3571)=0.6395-0.3605=0.279 \end{gathered}$

Therefore, the probability that sample mean is between 21.5 and 22.5 is 0.279

b. Given:

n = 25

Let's find the probability that the sample mean is between 21 and 22 minutes.

We have:

[tex]\begin{gathered} P(21Using the standard normal table, we have:[tex]\begin{gathered} P(-0.714286Therefore, the probability that sample mean is between 21 and 22 is 0.2625

c. Given:

n = 144

Let's find the probability the sample mean is between 21.5 and 22.5

[tex]\begin{gathered} P(21.5Therefore, the probability that sample mean is between 21.5 and 22.5 given a sample of 144 is 0.6086

d. Given:

Sample size in a = 25

Sample size in c = 144

The sample size in c is greater than the sample size in a so the standard error of the mean in (c) should be less than the standard error in (a).

As the standard error values become more concentrated