Administrators at the national headquarters of the Center for the Display of Vis

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 dollars. The data are normally distributed. 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 are between $278 and $349 per month? What percentage of balances exceed $349 per month? Should the auditing staff be concerned about the spending habits of this particular administrator?

Explanation / Answer

From information given, Xbar=278, s=33, find z scores corresponding to Xi=278 and 349 by substituting values in following z score formula.

z=(Xi-Xbar)/s; z1=(278-278)/33=0 and z2=(349-278)/33=2.15.

Find areas corresponding to z scores and subtract the smaller from the larger to find probability.

P(z1)=0.0000, P(z2)=0.4842; 0.4842-0.0000=0.4842. Therefore, 48.42% balances are between $278 and $349 per month.

To find what percenatge exceeds $349, substitute Xi with 349 and find z score.

z=(349-278)/33=2.15, P(z1)=0.4842; therefore, 48.42% of balances exceed $349 per month.

Since, in both cases, percentage of balances exceed $349 by 48.42%, the auditing staff should b econcerned by spending habit of particular administrator.

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