Time spent using e-mail per session is normally distributed, with u = 10 minutes and o = 3 minutes. Assume that the time spent per session is normally distributed. 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 9.8 and 10.2 minutes? 0.260 (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 9.5 and 10 minutes? 0.294 (Round to three decimal places as needed.) c. If you select a random sample of 100 sessions, what is the probability that the sample mean is between 9.8 and 10.2 minutes? 0.495 (Round three decimal places as needed.) 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 greater than in (a). As the standard error decreases, values become more concentrated around the mean. Therefore, the probability of a region that includes the mean will always increase when the sample size increases.
Time spent using e-mail per session is normally distributed, with u = 10 minutes and o = 3 minutes. Assume that the time spent per session is normally distributed. 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 9.8 and 10.2 minutes? 0.260 (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 9.5 and 10 minutes? 0.294 (Round to three decimal places as needed.) c. If you select a random sample of 100 sessions, what is the probability that the sample mean is between 9.8 and 10.2 minutes? 0.495 (Round three decimal places as needed.) 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 greater than in (a). As the standard error decreases, values become more concentrated around the mean. Therefore, the probability of a region that includes the mean will always increase when the sample size increases.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please answer for the boxes in D.
Transcribed Image Text:Time spent using e-mail per session is normally distributed, with µ= 10 minutes and o = 3 minutes. Assume that the time
spent per session is normally distributed. 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 9.8 and 10.2
minutes?
0.260 (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 9.5 and 10
minutes?
0.294 (Round to three decimal places as needed.)
c. If you select a random sample of 100 sessions, what is the probability that the sample mean is between 9.8 and 10.2
minutes?
0.495 (Round to three decimal places as needed.)
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 greater than in (a). As the standard error decreases , values become more
concentrated around the mean. Therefore, the probability of a region that includes the mean will always increase when
the sample size increases.
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