Question

A dentist is interested in obtaining information about delinquent (past due) accounts. Since the practice opened 10 years ago, delinquent accounts are normally distributed with an average of 40 days and a variance of 196.00 days. The dentist randomly selected a sample of 28 delinquent accounts with an average of 47 days.

a) The dentist wants to know what average number of days is less than 36% from the past 10 years.


b) Is the average days from the sample of 28 less than the 36% average from the past 10 years?

Answer 1

a) Here, = = 14

P(X < x) = 0.36

Or, P((X - )/ < (x - )/) = 0.36

Or, P(Z < (x - 40)/14) = 0.36

Or, (x - 40)/14 = -0.36

Or, x = -0.36 * 14 + 40

Or, x = 34.96

b) No, the average days from the sample of 28 is not less than the 36% average from the past 10 years.