Question 2 d) and question 3 a-d x MCA selective college woul x VA Homework 2 Bo
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Question 2 d) and question 3 a-d
x MCA selective college woul x VA Homework 2 Boise State IWelcome x Secure https://www.webassign.net/web/Student/Assignment-Responses/submit?dep 1 Previous Answers MIntroStat8 5 068 Ask Your Teacher 4/4 points My Notes A selective college would like to have an entering class of 950 students. Because not all students who are offered admission accept, the college admits more than 950 students. Past experience shows that about 75% of the students admitted will accept. The college decides to admit 1200 students. Assuming that students make their decisions independently, the number who accept has the B(1200, 0.75) distribution. If this number is less than 950, the college will admit students from its waiting list (a) What are the mean u and the standard deviation o of the number X of students who accept? 900 (b) Use the normal approximation to find the probability that at least 810 students accept. (Round your answer to four decimal places.) 0.9999 (c) The college does not want more than 950 students. What is the probability that more than 950 will accept? (Round your answer to four decimal places.) 0.0003 (d) If the college decides to increase the number of admission offers to 1,340, what is the probability that more than 950 will accept? (Round your answer to four decimal places 0.9474 eBook 0/4 points Previous Answers MIntroStat8 5.E.071 My Notes Ask Your Teacher Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of answers to different questions are independent. Jodi is a good student for whom p- 0.83 (a) Use the Normal approximation to find the probability that Jodi scores 77% or lower on a 100-question test. (Round your answer to four decimal places 0.001 (b) If the test contains 250 questions, what is the probability that Jodi will score 7 or lower? (Use the normal approximation. Round your answer to four decimal places. (c) How many questions must the test contain in order to reduce the standard deviation of Jodi's proportion of comect answers to half its value for a 100-item test? questions (d) Laura is a weaker student for whom p 0.78. Does the answer you gave in (c) for standard deviation of Jodi's score apply to Laura's standard deviation also? Yes, the smaller p for Laura has no effect on the relationship between the number of questions and the standard deviation. No, the smaller p for Laura alters the relationship between the number of questions and the standard deviation. eBook 0:15 PM Bu 3/1/2017Explanation / Answer
Solution:
2)
d)P ( X > 950 ) = P ( z > ( p - p )÷ (pq/n) )
= P(Z> 950-1340(0.75)/(1300(0.75)(0.25))
= P ( z > -3.52281 = 1-0.521794
= 0.4782
3)
(a) Mean = np = 100(.83) = 83
Standard deviation = sqrt [np(1-p)] = sqrt[100(.83)(.17)] = 3.7563
We want to find: P( x <= 77)
= 83
= 3.7563
standardize x to z = (x - ) /
P(x < 77) = P( z < (83-77) / 3.7563)
= P(z < 1.5973) = 0.8094
(From Normal probability table)
b) Mean = np = 250(.83) = 207.5
Standard deviation = sqrt [np(1-p)] = sqrt[250(0.83)(0.17)] = 5.9392
77% of 250 = 192.5
P( x <= 192.5) =
= 207.5
= 5.9392
standardize x to z = (x - ) /
P(x < 200) = P( z < (192.5-207.5) / 5.9392)
= P(z < -2.5255) = 0.0057
(From Normal probability table)
c) Mean = np = 100(.83) = 83
Standard deviation = sqrt [np(1-p)] = sqrt[100(.83)(.17)] = 3.756327
The standard deviation for proportions (not counts) in the 100 question test is 0.037563 (I used the
formula for proportions).
Half of that is 0.0187815.
0.0187815 = sqrt(0.17(0.83)/n) solve for n.
n = 400
d) Yes, the smaller p for Laura has no effect on the relationaship between the number of questions and the standard deviation.
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