# Finding some probabilities

The amount of time a bank teller spends with each customer has a population mean mx = 3.1 minutes and population standard deviation sx = 0.4 minute.

a) What is the probability that for a randomly selected customer 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 sample means) expected to be? What is expected to be the shape of the distribution of sample means? Give reasons for all your answers.

c) If a random sample of 64 customers is selected, what is the probability that the sample mean would exceed 3 minutes?

Source: Statistics for Business and Economics by Berenson and Levine. Second Edition. Chapter 9 Page 318. Ally and Bacon. 1993

please show work

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#### Solution Preview

The amount of time a bank teller spends with each customer has a population mean mx = 3.1 minutes and population standard deviation sx = 0.4 minute.

a) What is the probability that for a randomly selected customer the service time would exceed 3 minutes?

Let X be the service time. Then the probability that for a randomly selected customer the service time would exceed 3 minutes is

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#### Solution Summary

This solution consists of finding probabilities using sampling distribution.