Question

If 37% of high school students said that they exercise regularly, find the probability that 5 randomly selected high school students will say that they exercise regularly. Would you consider this event likely or unlikely to occur?

Answer 1

Very unlikely to occur

1) In this problem, let's find the binomial probability of that event to take place.

$\begin{gathered} P(X=5)=\binom{5}{5}(0.37)^5(1-0.37)^{5-5}= \\ P(X=5)=1\cdot(0.37)^5(1-0.37)^{5-5}= \\ P(X=5)=0.37^5\mleft(0.63\mright)^{5-5} \\ P(X=5)=0.0069343957 \end{gathered}$

2) Note the binomial probability of that event happening is very very low.

3) So we can state that this event is very unlikely to occur