The president of Doerman Distributors, Inc., believes that 25% of the firm’s ord

Question

The president of Doerman Distributors, Inc., believes that 25% of the firm’s orders come from first-time customers. A random sample of 200 orders will be used to estimate the proportion of first-time customers. Assume that the president is correct and p = 0.25.

a. What is the sampling distribution of p for this study?

b. What is the probability that the sample proportion p will be between .20 and .40?

c. What is the probability that the sample proportion will be between .25 and .35?

Label your answers with the appropriate mathematical notation .

**PLEASE NOTE** - I am using Excel and it is CRUCIAL that I know the excel functions to discover the answers. PLEASE HELP ME UNDERSTAND THIS BY LISTING THEM!!! Finding the answer isn't as hard for me as being able to input the functions via excel. THANK YOU SO MUCH!!!!

Explanation / Answer

Solution:

b) P(0.2<phat<0.4)

=P((0.2-0.25)/sqrt(0.25*0.75/100) <(phat-p)/[p*(1-p)/n] <(0.4-0.25)/sqrt(0.25*0.75/100))

=P(-1.16<Z<3.46)

= 0.8767

c) P(0.25<phat<0.35)

=P((0.25-0.25)/sqrt(0.25*0.75/100) <(phat-p)/[p*(1-p)/n] <(0.35-0.25)/sqrt(0.25*0.75/100))

=P(0<Z<2.31)

= 0.4896

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