# Question: A random sample of 16 junior managers in the offices

A random sample of 16 junior managers in the offices of corporations in a large city center was taken to estimate average daily commuting time for all such managers. Suppose that the population times have a normal distribution with a mean of 87 minutes and a standard deviation of 22 minutes.

a. What is the standard error of the sample mean commuting time?

b. What is the probability that the sample mean is fewer than 100 minutes?

c. What is the probability that the sample mean is more than 80 minutes?

d. What is the probability that the sample mean is outside the range 85 to 95 minutes?

e. Suppose that a second (independent) random sample of 50 junior managers is taken. Without doing the calculations, state whether the probabilities in parts (b), (c), and (d) would be higher, lower, or the same for the second sample. Sketch graphs to illustrate your answers.

a. What is the standard error of the sample mean commuting time?

b. What is the probability that the sample mean is fewer than 100 minutes?

c. What is the probability that the sample mean is more than 80 minutes?

d. What is the probability that the sample mean is outside the range 85 to 95 minutes?

e. Suppose that a second (independent) random sample of 50 junior managers is taken. Without doing the calculations, state whether the probabilities in parts (b), (c), and (d) would be higher, lower, or the same for the second sample. Sketch graphs to illustrate your answers.

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