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 third quartile of ages of cars in the lot. This means you will have to find the value such that $\frac{3}{4}or75\%$,of the cars are at most (less than or equal to) that age.

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

b. Find the value k such that$P(x<K)=0.75$

c. The third quartile is _____

Short answer

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

b. Value of K = 7.25

c. The third quartile is 7.25

Step-by-step solution

Scenario Description

Here 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; $0.5<x<9.5$

Here $$\begin{gathered} a=0.5 \\ b=9.5 \end{gathered}$$

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

Step Representation of Graph

The graph of the third percentile will be as follows;

Value of K

The value of K for Third percentile will be as follows;

$\begin{array}{rcl}P(x& <& k)=Base\times Height\\ 0.75& =& \left(k-0.5\right)\times \left(\frac{1}{9}\right)\\ k& =& (9\times 0.75)+0.5\\ & =& 7.25\\ & & \end{array}$