Chapter 13, Problem 14CT

To determine

The probability that randomly selected students at the college is between $18$ and $20$ years old, if the age distribution of the student at a community college is as follows;

$\begin{array}{ccccccc}\text{Age}& \text{17}\text{and}\text{under}& 18-20& 21-24& 25-34& 35-64& \text{65}\text{and}\text{over}\\ \text{Probability}& 0.03& ???& 0.23& 0.29& 0.25& 0.01\end{array}$.

Answer to Problem 14CT

Solution:

The probability that randomly selected students at the college is between $18$ and $20$ years old is $0.19$.

Explanation of Solution

Given information:

The age distribution of the students at a community college is as follows;

$\begin{array}{ccccccc}\text{Age}& \text{17}\text{and}\text{under}& 18-20& 21-24& 25-34& 35-64& \text{65}\text{and}\text{over}\\ \text{Probability}& 0.03& ???& 0.23& 0.29& 0.25& 0.01\end{array}$.

Explanation:

The age distribution of the students at a community college is as follows;

$\begin{array}{ccccccc}\text{Age}& \text{17}\text{and}\text{under}& 18-20& 21-24& 25-34& 35-64& \text{65}\text{and}\text{over}\\ \text{Probability}& 0.03& ???& 0.23& 0.29& 0.25& 0.01\end{array}$.

Denote the probability that randomly selected students at the college is between $18$ and $20$ years old by $x$.

The sum of probabilities must be equals $1$.

Thus, $0.03+x+0.23+0.29+0.25+0.01=1$.

$\Rightarrow 0.81+x=1$.

$\Rightarrow x=1-0.81=0.19$.

Therefore, the probability that randomly selected students at the college is between $18$ and $20$ years old is $0.19$.