Question

The mean amount purchased by a typical customer at Churchill's Grocery Store is $21.00 with a standard deviation of $7.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 42 customers, answer the following questions.





(a)


What is the likelihood the sample mean is at least $22.50? (Round z value to 2 decimal places and final answer to 4 decimal places.)





Probability







(b)


What is the likelihood the sample mean is greater than $20.00 but less than $22.50? (Round z value to 2 decimal places and final answer to 4 decimal places.)





Probability







(c)


Within what limits will 99 percent of the sample means occur? (Round your answers to 2 decimal places.)





Sample mean



and

Answer 1

The mean amount purchased by a typical customer at Churchill's Grocery Store is $21.00 with a standard deviation of $7.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 42 customers, answer the following questions.

(a) What is the likelihood the sample mean is at least $22.50? (Round z value to 2 decimal places and final answer to 4 decimal places.)

Probability 41.52%

Shaded area: 0.415162

(b) What is the likelihood the sample mean is greater than $20.00 but less than $22.50? (Round z value to 2 decimal places and final answer to 4 decimal places.)

Probability 14.16%

Normal Distribution

Mean: 21

Sd 7

Above 22.5

Below 1

Between 20 and 22.5

Outside -1 or 1

Shaded area: 0.141636