The average operating life of a popular brand of tablets is know to be 2000 days, with a standard deviation of 150 days. Suppose you want to pick a random sample of 49 tablets from this brand. (a) What is the mean and standard error of the sampling distribution of the sample mean X¯ for a sample size of 49?  (b) What is the probability that such a sample mean will be within 50 days of the population mean?  (c) What is the probability that such a sample mean is less than 1975?  (d) What value of the sample mean will only be exceeded 6% of the time?

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