Question

Administrators at the national headquarters of the Center for the Display of Visual Arts are authorized to make small work-related purchases using purchasing cards. The average amount administrators charge to their cards per month is $278 with a standard deviation of $33. The data are normally distributed. (a) The auditing staff at the center is concerned with the spending patterns of an administrator who has averaged $349 per month in charges. What percentage of balances exceed $349 per month? (b) Should the auditing staff be concerned about the spending habits of this particular administrator? (c) The auditors want to give the administrators some guidance on what is typical spending on the purchasing cards. Help them find a range that includes the middle 90% of monthly balances.

Answer 1

Here we have

(A)

The z-score for X = 349 is

The percentage of balances exceed $349 per month is

P(X > 349) = P(z > 2.15) =1- P(z <= 2.15) = 1 - 0.9842 = 0.0158

Answer: 1.58%

(b)

Yes because only 1.58% administrators spend more than this particular administrator. This is unusually high.

(c)

Here we need z-scores that have 0.90 area between them. z-scores -1.645 and 1.645 have 0.90 area between them. So required interval is

Answer: ($223.72, $332.29)