5.5 Practice 1: uniform distribution

What is being measured here?

In words, define the Random Variable $X$ .

Are the data discrete or continuous?

The interval of values for $x$ is:

The distribution for $X$ is:

Write the probability density function.

Graph the probability distribution.

• a Sketch the graph of the probability distribution.

  

• b Identify the following values:
  • i Lowest value for $x$ :
  • ii Highest value for $x$ :
  • iii Height of the rectangle:
  • iv Label for x-axis (words):
  • v Label for y-axis (words):

Find the probability that a randomly chosen car in the lot was less than 4 years old.

• a Sketch the graph. Shade the area of interest.

  

• b Find the probability. =

Out of just the cars less than 7.5 years old, find the probability that a randomly chosen car in the lot was less than 4 years old.

• a Sketch the graph. Shade the area of interest.

  

• b Find the probability. =

What has changed in the previous two problems that made the solutions different?

Find the average age of the cars in the lot.

Find the third quartile of ages of cars in the lot. This means you will have to find the value such that $\frac{3}{4}$ , or 75%, of the cars are at most (less than or equal to) that age.

• a Sketch the graph. Shade the area of interest.

  

• b Find the value $k$ such that .
• c The third quartile is: