Suppose in a particular college, 60% of the student population is female.

Question

Suppose in a particular college, 60% of the student population is female.

(a) Calculate the probability that a class of 10 students will have exactly four females.

(b) Calculate the probability that a class of 10 students will contain five, six, or seven females.

(c) Calculate the probability that at least five students in a class of 10 will be female.

Answer 1

Your calculator should have the binomial distribution with options for the mass function (probability of a particular value) and distribution function(cumulative distribution - <= )

In Excel, this is binom.dist(x, n, p, 0 or 1); x is the number of successes, n the number of trials, p the probability of success on each trial, and 0 if mass function and 1 if cumulative.

You can also calculate each probability yourself using the binomial distribution function -

P(x) = C(n,x) p^x(1-p)^(n-x)

In this problem, p = .6 and n = 10 for all.

a) P(X = 4) = binom.dist(4, 10, .6, 0) = .1114

b) P(5 <= X <= 7) = P(X <= 7) - P(X <= 3) = binom.dist(7, 10, .6, 1) - binom.dist(3, 10, .6, 1) = .7779

c) P(X >= 5) = 1 - P(X <= 4) = 1 - binom.dist(4, 10, .6, 1) = .8338