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Probability and mean / standard deviation at electronics firm

The personnel office at a large electronics firm regularly schedules job interviews and maintains records of the interviews. From the past records, they have found that the length of a first interview is normally distributed with mean = 35 minutes and standard deviation = 6 minutes. Nine first interviews are usually scheduled per day.

a. Find the mean and standard deviation of the sampling distribution of the mean length of time of the nine interviews .
b. Find the probability that the average length of the nine interviews is less than 29 minutes.
c. Find the probability that the average length of the nine interviews is between 32 and 38 minutes.
d. Find the probability that the average length of the nine interviews is at least 39 minutes.
e. Find the probability that the average length of the nine interviews is at most 35 minutes.

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