# Solved:If 37% of high school students said that they exercise regularly, find the probability that 5 randomly selected

#### ByDr. Raju Chaudhari

Sep 20, 2020

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? Explain your answer.

#### Solution

Let $X$ denote the number of high school students who exercise regularly out of 5 randomly selected students.

Let $p$ denote the probability that high school students exercise regularly.

Given that $p=0.37$.

$X\sim B(n=5, p=0.37)$.

The probability mass function of $X$ is
$$P(X=x) = \binom{5}{x} (0.37)^x (1-0.37)^{5-x}, \; x=0,1,\cdots, 5.$$

The probability that 5 randomly selected high school students will say that they exercise regularly is

\begin{aligned} P(X= 5) & =\binom{5}{5} (0.37)^{5} (1-0.37)^{5-5}\ & = 0.0069\ \end{aligned}

Explanation: The probability 0.0069 is quite low. So it is unlikely to occur that 5 randomly selected high school students will say that they exercise regularly.