The president of Doerman Distributors, Inc., believes that 29% of the firm\'s or

Question

The president of Doerman Distributors, Inc., believes that 29% of the firm's orders come from first-time customers. A simple random sample of 100 orders will be used to estimate the proportion of first-time customers.

a. Assume that the president is correct and p = 0.29. What is the sampling distribution of p for this study? Select from 1 of the 3 answers below:

A normal distribution because np and n(1-p) are both greater than 5A normal distribution because np and n(1-p) are both greater than 5A non normal distribution

A normal distribution because np and n(1-p) are both greater than 5A normal distribution because np and n(1-p) are both less than 5A non normal distribution

A non-normal distribution

b. What is the probability that the sample proportion will be between .18 and .40 (to 4 decimals)?

c. What is the probability that the sample proportion will be between .23 and .35 (to 4 decimals)?

Explanation / Answer

here mean proportion =0.29

and std error =(p(1-p)/n)1/2 =0.0485

1) A normal distribution because np and n(1-p) are both greater than 5

b) P(0.18<P<0.40) =P((0.18-0.29)/0.0485<Z<(0.40-0.29)/0.0485)=P(-2.2696<Z<2.2696)=0.9884-0.0116 =0.9768

c) P(0.23<P<0.35) =P((0.23-0.29)/0.0485<Z<(0.35-0.29)/0.0485)=P(-1.2380<Z<1.2380)=0.8921-0.1079=0.7843

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.