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 59 days and a SD of 9 days. The dentist randomly selected a sample of 30 delinquent accounts with an average of 47 days.

a) The dentist wants to know what average number of days is more than 67% from the past 10 years.


b) Is the average days from the sample of 30 less than the 67% average from the past 10 years?
---Select--- na Yes No

Answer 1

We are given the delinquency period distribution here as:

a) From standard normal tables, we have here:
P(Z < 0.440) = 0.67

This means that 0.440 z score is more than 67% from past 10 years.

The average limit here is thus computed as:
= Mean + 0.440*Std Dev

= 59 + 0.440*9 = 62.96

Therefore 62.96 days is the required limit here.

b) The average number of days from the sample of 30 is 47 days which is clearly lower than 62.96 days. Therefore it is lower here and therefore the given statement is True. Yes is the correct answer here.