Question

A dentist is interested in obtaining information about delinquent (past due) accounts. Since the practice opened 12 years ago, delinquent accounts are normally distributed with an average of 47 days and a SD of 10 days. The dentist randomly selected a sample of 29 delinquent accounts with an average of 47 days.

a) The dentist wants to know what average number of days is less than 66% from the past 12 years.


b) Is the average days from the sample of 29 more than the 66% average from the past 12 years?

Answer 1

let X is value of delinquent accounts

so as given that X is normal distribution with

sample size =n=29

sample mean==47

a)

let "u" is average value that is less than 66% from the past 12 years so

now

from Z table

P(Z>-0.412)=0.66 so on comparing

so required value is 46.235

b)

sample avearge ==47

now

since only 50% of values less than the sample average hence its not more than 66% of averages