Question

A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues.

If 6 college freshmen are randomly selected, find the probability that exactly 3 support increased spending on environmental issues.

a. .0330

b. .1318

c. .7844

d. .9624

Answer 1

b. .1318

Explanation:

For each freshmen, there are only two possible outcomes. Either they support increased spending on enviromental issues, or they do not. The probabiliy of each freshmen supporting increased spending on environmental issues is independent from each other. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

In this problem we have that:

25 percent of college freshmen support increased spending on environmental issues. This means that
`p = 0.25`

If 6 college freshmen are randomly selected, find the probability that exactly 3 support increased spending on environmental issues.

This is
`P(X = 3)` when
`n = 6`. So

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 3) = C_(6,3)*(0.25)^(3).(0.75)^(3) = 0.1318`

So the correct answer is:

b. .1318