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

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