Question

The mean amount purchased by each customer at Churchill’s Grocery Store is $27 with a standard deviation of $9. The population is positively skewed. For a sample of 48 customers, answer the following questions:

a. What is the likelihood the sample mean is at least $29? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.)

b. What is the likelihood the sample mean is greater than $26 but less than $29? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.) c. Within what limits will 98% of the sample means occur? (Round the final answers to 2 decimal places.)

Answer 1

Since the sample size is 48 >30, we can use the CLT and approximate the distribution of the sample mean to be normal i.e.

i.e.

i.e.

i.e.

a.

We need to compute

. The corresponding z-value needed to be computed is:

Therefore, we get that

The following is obtained graphically:

b.

The following is obtained graphically:

c.

98% of the sample means will lie between

Calculated as:

The following is obtained graphically:

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