# 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.

Binomial Probability: find probabilities.

5.A marketing firm wants to target people who eat breakfast by sending out a new product. According to recent statistics three in four people eat breakfast. If the marketer sends out samples to 10 people selected at random, Find the probability using the binomial probability distribution formula. (Show all work)

a. Exactly 8 people eat breakfast

b. Exactly 3 people eat breakfast

6.According to a recent survey 30% of people are late for work on any given day. You are a manager of a department of 18 people. Find the probability

a. 3 will be late on a given day.

b. 0 will be late on a given day.

c. More than 1 person will be late on a given day

d. 2 or fewer will be late on a given day

7. Construct a binomial distribution chart and table showing all of the outcomes if a woman would like to know all possible outcomes of having 3 children. Also show this using a probability tree diagram.

a. What are the odds the second child is a boy?

b. What are the odds she has all 3 boys?

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