Question

Time spent using​ e-mail per session is normally​ distributed, with mu equals 8 minutes and sigma equals 2 minutes. Complete parts​ (a) through​ (d).

a. If you select a random sample of 25 ​sessions, what is the probability that the sample mean is between 7.8 and 8.2 ​minutes?

=0.3830 ​(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 7.5 and 8 ​minutes?

= 0.3944 ​(Round to three decimal places as​ needed.)

c. If you select a random sample of 200 ​sessions, what is the probability that the sample mean is between 7.8 and 8.2 ​minutes? ​

d. Explain the difference in the results of​ (a) and​ (c). Choose the correct answer below. 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). In​ general, as the standard deviation​ decreases, values become ........ concentrated around the mean.​ Therefore, the probability of a region that includes the mean will always ........ when the sample size increases.

Answer 1

µ = 8

c) n = 200

                                     

                                      = P(-1.41 < Z < 1.41)

                                      = P(Z < 1.41) - P(Z < -1.41)

                                      = 0.9207 - 0.0793

                                      = 0.8414

d) he 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 ....smaller..... than in​ (a). In​ general, as the standard deviation​ decreases, values become ...more..... concentrated around the mean.​ Therefore, the probability of a region that includes the mean will always ...increases..... when the sample size increases.