Question

A dentist is interested in obtaining information about delinquent (past due) accounts. Since the practice opened 6 years ago, delinquent accounts are normally distributed with an average of 53 days and a SD of 11 days. The dentist randomly selected a sample of 32 delinquent accounts with an average of 47 days.

a) The dentist wants to know what average number of days is more than 45% from the past 6 years.

Answer 1

a) P( > x) = 0.45

Or, P(( - )/() > (x - )/()) = 0.45

Or, P(Z > (x - 53)/(11/))= 0.45

Or, P(Z < (x - 53)/(11/)) = 0.55

Or, (x - 53)/(11/) = 0.13

Or, x = 0.13 * (11/) + 53

Or, x = 53.25