Question

3. If a population distribution is known to be normal, then it follows that:

A. The sample mean must equal the population mean B. The sample mean must equal the population mean for large samples C. The sample standard deviation must equal the population standard deviation D. All of the above E. None of the above

4. The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent more than 90 days overdue. The historical records of the company show that over the past 8 years 14 percent of the accounts are delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts. What is the probability that at least 30 accounts will be classified as delinquent?

A. 31.86% B. 18.14% C. 81.86% D. 63.72% E. 75.84%

5. In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03. If we randomly select three bolts from this process: What is the probability the mean length of the bolt is more than 3.16 inches?

A. 5.48% B. 97.72% C. 94.52% D. 44.52% E. 2.28%

Answer 1

3)E. None of the above

4)

here mean of distribution=μ=np=		35
and standard deviation σ=sqrt(np(1-p))=		5.49
for normal distribution z score =(X-μ)/σx

therefore from normal approximation of binomial distribution and continuity correction:

probability =

P(X>30)

=

P(Z>-0.91)=

1-P(Z<-0.91)=

1-0.1814=

0.8186 ~81.86%

5)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	3
std deviation   =σ=	0.173
sample size       =n=	3
std error=σx̅=σ/√n=	0.1000

probability =

P(X>3.16)

=

P(Z>1.6)=

1-P(Z<1.6)=

1-0.9452=

0.0548~5.48%