My Notes Ask Your Teacher booke bookshelf. He forgot to specify what type of Pet

Question

My Notes Ask Your Teacher booke bookshelf. He forgot to specify what type of Peter has 15 books an his bookshelf. In these 6 are math books and 9 are statistics books. He needs 4 books to show the government Inspectors so he asks his TA to pick 4 books off af his the 15 books. Let = the number of selected books which are math books. book so she randomly selects 4 of ts books. Let x i are math books ltistics boc a. What is the probability that none of the selected books are math books? b. What is the probability that fewer than 2 of the selected books are matn books? c. What is the expected vakue of x? d. What is the stancard deviation of X? e. What is the probabi ty that X is within1 standard devlation of its expected value? Add any comments below

Explanation / Answer

(a) The given distribution is hypergeometric distribution

where N = 15, n = 4 , K = 6 ,

here

Total books on shelf (N) = 15

(a) Pr(None of the books are math books) = Pr(all 4 books are statistics books)

Pr(None of the books are math books) = (9/15) * (8/14) * (7/13) * (6/12) = 6C09C4 /15C4 = 0.0923

(b) Pr(Fewer than two books are maths books) = Pr(no maths book) + Pr(1 math book)

= 6C09C4 /15C4 +  6C19C3 /15C4 = 0.0923 + 0.3692 = 0.4615

(c) E(X) = nK/N = 4 * 6/15 = 1.6

(d) Var(X) = n (K/N) [(N-K)/N] [ (N-n)/(N-1) ]

= 4 * (6/15) * (9/15) * (11/14)

= 0.7543

STD(X) = sqrt(0.7543) = 0.8685

(e) Number of students within 1 standard deviation of expected values are

+- = 1.6 +- 0.8685 = (0.7315, 2.4685) so it consists X = 1 and X =2

so  Pr(X < +- ) = Pr(X = 1) + Pr(X = 2)

= 6C19C3 /15C4 + 6C29C2 /15C4  = 0.3692 + 0.3956 = 0.7648

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