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.

Considering only the cars less than 7.5 years old, find the probability that a randomly chosen car in the lot was less than four years old.

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

b. Find the probability$P(x<\overline{)4}x<7.5)=$

Short answer

a. The graph, shade the area of interest.

b. The probability$P(x<\overline{)4}x<7.5)=0.5$

Step-by-step solution

Senario

As per Details give in the problem ;

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

Here in problem 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 for the given distribution function will be ;

$\begin{array}{rcl}f\left(x\right)& =& \frac{1}{b-a}\\ & =& \frac{1}{7.5-0.5}\\ & =& \frac{1}{7}\end{array}$

Graph

As per the above data the graph of probability function will be

The probability of function 

As per this the required probability will be;

$\begin{array}{rcl}P(x& <& \overline{)4}x<7.5)=Base\times Height\\ & =& \left(4-0.5\right)\left(\frac{1}{7}\right)\\ & =& 3.5\times \frac{1}{7}\\ & =& 0.5\end{array}$