Question 1(8 marks = 2 + 2 + 2 + 2)
A company is having a new website developed. In the final testing phase the download time to open the new home page is recorded for a large number of computers in home and office settings. The mean download time for the site is 2.5 seconds. Suppose that the download times forthe site are normally distributed with a standard deviation of 0.5 seconds. If you select a random sample of 30 download times,
a. What is the probability that the sample mean is less than 2.75 seconds?
b. What is the probability that the sample mean is between 2.70 and 2.90 seconds?
c. The probability is 80% that the sample mean is between what two values symmetrically distributed around the population mean?
d. The probability is 90% that the sample mean is less than what value?
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