# The mean amount purchased by a typical customer at Churchill

The mean amount purchased by a typical customer at Churchill's Grocery Store is $23.50 with a standard deviation of $5.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 50 customers, answer the following questions.

a. What is the likelihood the sample mean is at least $25.00?

b. What is the likelihood the sample mean is greater than $22.50 but less than $25.00?

c. Within what limits will 90 percent of the sample means occur

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#### Solution Preview

a. P(Xbar ≥ 25) = P(Z ≥ (25-23.5)/(5/sqrt(50))) = P(Z ≥ 2.12) = ...

#### Solution Summary

The solution provides detailed calculations and explanations for the problem.

The mean amount purchased by a typical customer at Churchill's Grocery Store is $23.50

with a standard deviation of $5.00. Assume the distribution of amounts purchased follows

the normal distribution.

The mean amount purchased by a typical customer at Churchill's Grocery Store is $23.50

with a standard deviation of $5.00. Assume the distribution of amounts purchased follows

the normal distribution. For a sample of 50 customers, answer the following questions.

a. What is the likelihood the sample mean is at least $25.00?

b. What is the likelihood the sample mean is greater than $22.50 but less than $25.00?

c. Within what limits will 90 percent of the sample means occur?