Question

The mean amount purchased by each customer at Summit bookstore is $35 with a standard deviation of $9. The population is positively skewed. For a sample of 42 customers, answer the following questions: a. What is the likelihood the sample mean is at least $39? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.) Sample mean b. What is the likelihood the sample mean is greater than $33 but less than $39? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.) Sample mean c. Within what limits will 98% of the sample means occur? (Round the final answers to 2 decimal places.)

Answer 1

a.

The following information has been provided:

We need to compute Pr(X≥39). The corresponding z-value needed to be computed is:

Therefore, we get that

The following is obtained graphically:

b.

We need to compute . The corresponding z-values needed to be computed are:

Therefore, we get:

The following is obtained graphically:

c.

The answer is between:

31.76933

and

38.23067

Using excel:

=NORM.INV(0.02/2,35,1.38873014965883)

and

=NORM.INV(1-0.02/2,35,1.38873014965883)

The following is obtained graphically:

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