A financial institution wishes to estimate the mean balances owed by its credit card customers. The population standard deviation is $300. If a 99 percent confidence interval is used and an interval of ± $75 is desired, how many cardholders should be sampled?
A)3382
B)629
C)87
D)107

Question

Quizplus · Accepted Answer

The formula for the required sample size is:
n = [Z * (σ / E)]^2

where Z is the z-score corresponding to the desired level of confidence (99% in this case), σ is the population standard deviation, and E is the desired margin of error.

Substituting the given values:

n = [2.576 * (300 / 75)]^2
n = 106.89

Rounding up to the nearest integer, the required sample size is 107. Therefore, the best choice is D.

A Financial Institution Wishes to Estimate the Mean Balances Owed