1) You are interested in studying the award process of the financial aid office

Question

1) You are interested in studying the award process of the financial aid office of the university. Not every student who applies for a certain type of aid receives that honor. The probability that an applicant receives the award is 46%. Out of a sample of 28 students that applies for this type of award, find the following probabilities (12 points—6 problems, 2 points each)

a) the probability that exactly 15 applicants receives the award

b) the probability that at least 18 applicants receive the award

c) the probability that fewer than 12 applicants receive the award

d) the probability that between 17 and 25 applicants (inclusive on both ends) receive the award

e) Find the mean number of applicants that receives the award.

f) Find the standard deviation of the number of applicants that receives the award.

Explanation / Answer

Solution:- given that n = 28, p =0.46

a) P( X = 15) = 0.1086

b) P(X >= 18) = 0.0399

c) P(X < 12) = 0.3021

d) P( 17 <= X <= 25) = P(17)+ P(18) + P(19) + P(20) + P(21) + P(22) + P(23) + P(24) + P(25)

= 0.0452+0.0235+0.0105+0.0040+0.0013+0.0004+0.0001+0.0000+0.0000

= 0.085

e) mean = np = 28*0.46 = 12.88

f) sd = sqrt(np(1-p)) = sqrt(28*0.46*(1-0.46)) = 2.6373

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