Lori jeffrey is a successful sales representative for a...

Lori Jeffrey is a successful sales representative for a major publisher of college textbooks. Historically, Lori obtains a book adoption on 25% of her sales calls. Viewing her sales calls for one month as a sample of all possible sales calls, assume that a statistical analysis of the data yields a standard error of the proportion of 0.0625. (a) How large was the sample used in this analysis? That is, how many sales calls did Lori make during the month? sales calls b. indicate the sample proportion of book adoptions obtained during the month. Show the sampling distribution of p. (c) Using the sampling distribution of p, compute the probability that Lori will obtain book adoptions on 20% or more of her sales calls during a one-month period. (Round your answer to four decimal places.)

Transcript

00:01 Hi, i'm david and i'm to help you answer your question.

00:03 Now let me bring up your question here.

00:06 In the question here we are going to discuss about the sampling distribution on the sample proportion.

00:11 Let me remind you that under certain condition, the p -hard will be approximately to the normal.

00:17 Well, we have the mean motp h equal to the population proportion and we have the standard division on the p -hr sometimes called the standard error.

00:29 It will equal to square root of p times 1 minus b over the n.

00:36 Now in this question here we are given that the p equal to the 25 % and it will equal to the 1725 we're given the standard error of the proportion equal to the zepon 0625.

00:53 Now in the question a asks let you find the same process end.

00:59 Now because the standard error equal to this one, so 0 .0 .06, 25, and by the formula equal to the square root of the p equal to the 0 .25, 1 minus 0 .25, over the n.

01:15 So from here, we can find that the square on both sides, we will have the n.

01:22 It will equal to the 0 .25 times with the z upon 75, divided by the zabon 0 .0.

01:30 0625 square and if we compute it we will get equal to 025 times 075 divided 06 25 square equal to the 48 so n equal to the 48 that will be the answer for the 8 now for the p here we are going to indicate the sample portion on the book in treatment and we have by the formula the p .00 be approximately to the normal that will be with the mean on the pheed equal to the p equal to the zon 25 and the standard division on the p hath equal to the 06, 25.

02:15 And from the question c, once you find the probability that 20 % are more, so will be the p hath will be quite equal to the zabon 2.

02:27 Now to find this probability, i will remind you that it will tend to the p h minus the mean of the standard division we have 10 standard no more.

02:37 So if we use this formula, we will convert that p ht into the z.

02:42 So we will take the 0 .2, we minus the p will be the 0 .25, over the standard division equal to the 0 .625...

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