Question

In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the probability that exactly 2 students have experienced math anxiety is

a.0.3020
b.0.5
c.0.2634
d.0.2013
e.1

Answer 1

a.0.3020

Explanation:

For each student, there are only two possible outcomes. Either they have experienced feeling of math anxiety, or they have not. The students are chosen at random, which means that the probability of a student having experienced feelings of math anxiety is independent from other students. So we use the binomial probability distribution to solve this question.

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.

20% of the students have experienced feelings of math anxiety.

This means that
`p = 0.2`

If you take a random sample of 10 students from this population, the probability that exactly 2 students have experienced math anxiety is

This is
`P(X = 2)` when
`n = 10`

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

`P(X = 2) = C_(10,2).(0.2)^(2).(0.8)^(8) = 0.3020`

So the correct answer is:

a.0.3020