SOLUTION: John surfs the website on a regular basis. Suppose the time he spent surfing the website per day is normally distributed, µ = 8 minutes and σ = 2 minutes. If you select a random

Question 1160975: John surfs the website on a regular basis. Suppose the time he spent surfing the website per day is normally distributed, µ = 8 minutes and σ = 2 minutes. If you select a random sample of 4 sessions,
a. What is the probability that the sample mean is less than 8 minutes?
b. What is the probability that sample mean is between 8 and 10 minutes?
c. If you select a random sample of 16 sessions, what is the probability that a as sample mean is between 8 and 9 minutes?
d. Explain the differences in the results of (b) and (c).

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
a. 50%, since E(X bar)=8 minutes
z=(x bar-mean)/sigma/sqrt(n)
sigma/sqrt(n)=2/2=1
so b is looking at 8 and 10 minutes with sd 1
this is z between 0 and 2, which is 0.4772.
for 16 now the sd will be 2/sqrt(16)=0.5
and the same probability of 0.4772 will occur.
It is much more likely that the sampling distribution will be narrower and distances from the expected value of 8 (in this instance) won't be as much as the sample size increases.
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