A dentist wants to find the average time taken by one of her hygienists to take X-rays and clean teeth for patients. She recorded the time to serve 24 randomly selected patients by this hygienist. The data (in minutes) are as follows:

Assume that such times for this hygienist for all patients are approximately normal.
a. What is the point estimate of the corresponding population mean.
b. Construct a 99% confidence interval for the average time taken by this hygienist to take X-rays and to clean teeth for all patients.

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36.80 39.80 38.60 38.30 34.30 32.60 38.70 34.50 37.00 36.80 40.90 33.80 37.10 33.00 35.10 38.20 36.60 38.80 39.60 39.70 35.10 38.20 32.70 39.50