The president of Doerman Distributors, Inc., believes that 28% of the firm\'s or

Question

The president of Doerman Distributors, Inc., believes that 28% 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 = 0.28. What is the sampling distribution of p for this study? b. What is the probability that the sample proportion will be between .16 and .40 (to 4 decimals)? c. What is the probability that the sample proportion will be between .21 and .35 (to 4 decimals)?

Explanation / Answer

a) sampling distribution of p for this study will be approximately normal with

estimated proportion =0.28

and standard error of proportion =sqrt(p*(1-p)/n)=0.0449

b)as z score=(phat-p)/std error

P(0.16<P<0.40)=P(-2.67<Z<2.67)=0.9962-0.0038 =0.9924 ( please try 0.9925 if this comes wrong due to rounding error)

c)

P(0.21<P<0.35)=P(-1.56<Z<1.56)=0.9406-0.0594 =0.8812 (please try 0.8810 if this comes wrong due to rounding error)

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