The amount of time a bank teller spends with each customer has a population mean ?_x=3.2 minutes and population standard deviation ?_x=0.25 minute.a)If a customer is randomly selected, what is the probability that the service time would exceed 3 minutes?b)If many samples of 64 were selected, what are mean and standard error of the mean (standard deviation of the sample means) expected to be? What is the expected shape of the distribution of sample means? Justify your answer.c) If a random sample of 64 customers is selected, what is the probability that mean service time would exceed 3 minutes? (hint: one-side of the normal distribution is 50%).
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