Question

In a certain​ state, 32.2​% 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 3 belong to an ethnic minority. b. Three or fewer belong to an ethnic minority. c. Exactly 5 do not belong to an ethnic minority. d. Six or more do not belong to an ethnic minority. a.​ P(3​)equals nothing

Answer 1

0.2638,0.5902,0.1250,0.5902

Explanation:

Given that in a certain ​ state, 32.2​% of all community college students belong to ethnic minorities.

i.e. probability for any random college student to belong to ethnic minorities

=0.322

This is constant as each student is independent of the other

X no of college students belong to ethnic minorities in the sample of 10 is

Bin (10, 0.322)

a) Exactly 3 belong to an ethnic minority.

`=P(X=3)\\=0.2638`

b. Three or fewer belong to an ethnic minority.

=
`P(X\leq 3)\\=0.5902`

c. Exactly 5 do not belong to an ethnic minority.

`P(X'=5)=P(X=5)\=0.1250`

d. Six or more do not belong to an ethnic minority.

`P(X'\geq 6)\\=P(X<4)\\=0.5902`