Question

In a certain state, 36.2% of all community college students belong to ethnic minorities. Find the probabilities of the following results in a random sample of 10 of the community college students. a. Exactly 2 belong to an ethnic minority. b. Three or fewer belong to an ethnic minority. c. Exactly 6 do not belong to an ethnic minority. d. Six or more do not belong to an ethnic minority. a. P(2) = (Round to four decimal places as needed.) b. P(three or fewer belong to an ethnic minority) = (Round to four decimal places as needed.) . c. P(exactly 6 do not belong to an ethnic minority) (Round to four decimal places as needed.) d. P(six or more do not belong to an ethnic minority) (Round to four decimal places as needed.)

Answer 1

Givena X. Mamber of students belong to minorities. ethnic P = + its 0.362 Binomial (n=co, p=0.362) probeebility mass furction is given by - P(x = x) = - (10) (0.36280 (1 -0.36272 ca) 7 Find the belong to an p(x - 2) = probability that exactly a eithnic minority ( 10 (0.362) 2 (1-0.362) р ( 2 ) . Цу 0.1619 p(2) = 3 These or rewer belong to an ethnic family plx53) - PCt =o) + P(x = 1 + P (A=2) o tplt=3 = ( 109.01-0362307 (19].cosa'-0.362) + (1) 60-363) <1-10-262) + ( 69c0-363*30-34337 - 0.0112 + 0.0634 +0.1619 + 0.2449 P(+3) = 0.4814

T.P( three or fever belong to arethnic I tamity minority) = 0.48 14 c) Exeactly 6 do not belong to con ethnic family. Pcx76) 1-pc+=61 = 1-(10] (0.362) 8 (1-0.58) = " - 0.0783 A C+76) = 0.9217 P ( exactly 6 do not belong to an e thric & minority) = 0.9217 a) sit or more de not belong to an ethnic minority - P(x <6) = P(x 20)+pex=1) +PC+=2 - pet-3 tpet=4) FPCT =5) 0.0112 for 0634 to.1619 +0.2444 +0.244 g t o.1656 = 0.8 goz psitor more do not ethnic minority ] = an belong to 0.89 02