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As part of the qualification process, prospective Santa Barbara County Lifeguards are required to pass an open-ocean swimming test. The times for the swim test are normally distributed with a mean of 34.6 minutes and a standard deviation of 8.25 minutes. A random sample of 12 times were taken from the 2020 qualification event, and the sample mean time calculated.
a. What is the distribution of the sample mean time?
b. What is the expected value of the sample mean time?
c. What is the variance of the sample mean time?
d. What is the probability that the sample mean time is less than 30 minutes?
e. What is the probability that the sample mean time is between 30 and 34 minutes (inclusive)?
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