In a certain state 38 of all community college students belo

In a certain state, 38% 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.

Solution

Here\' how to solve the question.:

The question asks for the application of pdf function of binom distribution

P(X=k) = nCk * (p)^k (1-p)^n-k

In a certain state, 38% 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.

P(X=3) = 10C3(.38)^3(1-.38)^7 = .232

b. Three or fewer belong to an ethnic minority.

P(X<=3) = .4336

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

P(X\'=5) =10C5(.62)^5(.38)^5 = .1829

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

P(X\'>=6) = 0.6823