Question

Use the following information to answer the next eleven exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years.

Find the probability that a randomly chosen car in the lot was less than four years old;

a. Sketch the graph, and shade the area of interest.

b. Find the probability. $P(x<4)$

Short answer

a. The graph is as follows;

b. The Probability of$P(x<4)=0.389$

Step-by-step solution

Data Analysis

As per given Data;

Uniform distribution has been considered within the age of cars in staff parking lot of suburban college

Thus;

The age of the cars in suburban college is represented with X, and x as intervals.

Therefore; $0.5<x<9.5$

Hence the probability distribution function or the height of the graph will be;

$\begin{array}{rcl}f\left(x\right)& =& \frac{1}{b-a}\\ & =& \frac{1}{9.5-0.5}\\ & =& \frac{1}{9}\end{array}$

Graph

As per the above calculation Graph of $P(x<4)$can be represented as;

Probability of P(x<4)

The required probability can be calculated as;

$\begin{array}{rcl}P(x& <& 4)=Base\times Height\\ & =& (4-0.5)\left(\frac{1}{9}\right)\\ & =& 3.5\times \frac{1}{9}\\ & =& 0.389\end{array}$