Insurance company records indicate that 10% of its policyholders file claims
Involving theft or robbery of personal property from their homes. Suppose a random
Sample of 400 policyholders is selected. The probability that the sample proportion of
Policyholders filing claims involving theft or robbery from their homes is less than 8% is
A) .0918
B) .1333
C) .4082
D) .0517
E) .7892

Question

Quizplus · Accepted Answer

The sample proportion follows a normal distribution with mean 0.10 and standard deviation sqrt((0.10*0.90)/400). Using the z-score formula, we find the probability that the sample proportion is less than 0.08, which corresponds to a z-score of approximately -1.34. The probability of a z-score less than -1.34 is approximately 0.0918.

Insurance Company Records Indicate That 10% of Its Policyholders File