A random sample of junior managers working for corporations in a large city centre was taken in order to estimate the average daily commuting times for all such managers. Suppose that the population times for all such managers has mean minutes and standard deviation minutes. Answer the following questions, rounding your answers to two decimal places where appropriate.
(a)
Find the standard error of the sample mean commuting time.
(b)
Consider that the sampling distribution of the sample mean follows the normal distribution. The probability that the sample mean is less than minutes is shown as the shaded area in which of the following graphs?
Choose
(1)
(2)
(1)
(2)
(Click on a graph to enlarge it.)
(c)
Find the probability that the sample mean is less than minutes.
(d)
When the sample size is increased, the standard error of the sample mean will:
A.
increase
B.
decrease
C.
stay the same
(e)
When the sample size is increased, the probability that the sample mean is less than minutes will:
A.
decrease
B.
increase
C.
stay the same
You can earn partial credit on this problem.