Question

In a certain​ state,

37.637.6​%

of all community college students belong to ethnic minorities. Find the probabilities of the following results in a random sample of

1010

of the community college students.a. Exactly

33

belong to an ethnic minority.

b. Three or fewer belong to an ethnic minority.

c. Exactly

66

do not belong to an ethnic minority.d.

SixSix

or more do not belong to an ethnic minority.

a.

​ P(33​)equals=nothing

​(Round to four decimal places as​ needed.)

b.​ P(three or fewer belong to an ethnic

​minority)equals=nothing

​(Round to four decimal places as​ needed.)

c.​ P(exactly

66

do not belong to an ethnic

​minority)equals=nothing

​(Round to four decimal places as​ needed.)

d.

​ P(sixsix

or more do not belong to an ethnic

​minority)equals=nothing

​(Round to four decimal places as​ needed.)

Answer 1

p = 0.376

n = 10

P(X = x) = 10Cx * 0.376^x * (1 - 0.376)^10-x

a) P(X = 3) = 10C3 * 0.376³ * (1 - 0.376)⁷ = 0.2350

b) P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

                  = 10C0 * 0.376⁰ * (1 - 0.376)¹⁰ + 10C1 * 0.376¹ * (1 - 0.376)⁹ + 10C2 * 0.376² * (1 - 0.376)⁸ + 10C3 * 0.376³ * (1 - 0.376)⁷

                  = 0.4441

c) p = 1 - 0.376 = 0.624

P(X = 6) = 10C6 * 0.624⁶ * (1 - 0.624)⁴ = 0.2478

d) P(X > 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

                  = 10C6 * 0.624⁶ * (1 - 0.624)⁴ + 10C7 * 0.624⁷ * (1 - 0.624)³ + 10C8 * 0.624⁸ * (1 - 0.624)² + 10C9 * 0.624⁹ * (1 - 0.624)¹ + 10C10 * 0.624¹⁰ * (1 - 0.624)⁰

                  = 0.6919