The total study time for a statistics assignment in a popula

The total study time for a statistics assignment in a population of college students was approximately Normally distributed with a mean of 7.62 hours and standard deviation of 1.85 hours. Suppose you plan to take an SRS of size 250 and compute the average study time. (a) What is the mean and standard deviation (standard error) of the sample mean? (b) What is the probability of selecting a sample that has a sample mean that shows that they studied 6.0 hours or less?

Solution

(a) What is the mean and standard deviation (standard error) of the sample mean?

mean=7.62

standard error = s/vn

=1.85/sqrt(250)

=0.1170043

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(b) What is the probability of selecting a sample that has a sample mean that shows that they studied 6.0 hours or less?

P(xbar<6) = P((xbar-mean)/(s/vn) <(6-7.62)/0.1170043)

=P(Z<-13.85) =0 (from standard normal table)