According to a social media blog, time spent on a certain social networking webs

Question

According to a social media blog, time spent on a certain social networking website has a mean of 23 minutes per visit. Assume that time spent on the social networking site per visit is normally distributed and that the standard deviation is 7 minutes. Complete parts (a) through (d) below. a.t you select a random sample of 25 sessions, what is the probability that the sample mean is between 22.5 and 23.5 minutes? (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 behween 22 and 23 minutes? (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 22.5 and 23.5 minutes? Round to three decimal places as needed.) . 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 concentrated around the mean. Therefore, the probability that the sample mean will fall in a region that includes the population mean will always than in (a). As the standard error "valos become moro when the sample size increases.

Explanation / Answer

Solution:- Given that mean = 23 , standard deviation = 7

a. for n = 25
P(22.5 < X < 23.5)
= P((22.5 - 23)/(7/sqrt(25)) < (X - ?)/(?/sqrt(n)) < (23.5 - 23)/(7/sqrt(25))
= P(-0.3571 < Z < 0.3571)
= 0.2812

b. For n = 25
P(22 < X < 23) = P((22 - 23)/(7/sqrt(25)) < Z < (23 - 23)/(7/sqrt(25))
= P(-0.7143 < Z < 0)
= 0.2611

c. For n = 100

P(22.5 < X < 23.5) = P((22.5 - 23)/(7/sqrt(100)) < Z < (23.5 - 23)/(7/sqrt(100))
= P(-0.7143 < Z < 0.7143)
= 0.5222

d) The sample size in (c) is greater than the sample size in (a).so the standard error of the mean in is(C) smaller than in (a) As the standard error volume become more concentrated around the mean.therefore,the probability that the sample mean will fall in a region that includes the population mean wil always be more when the sample size increase
  
  

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