# 5.12 Continuous random variables: practice 1

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In this module the student will explore the properties of data with a uniform distribution.

## Student learning outcomes

• The student will analyze data following a uniform distribution.

## Given

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.

## Describe the data

What is being measured here?

The age of cars in the staff parking lot

In words, define the Random Variable $X$ .

$X$ = The age (in years) of cars in the staff parking lot

Are the data discrete or continuous?

Continuous

The interval of values for $x$ is:

0.5 - 9.5

The distribution for $X$ is:

$X$ ~ $U\left(0\text{.}5,9\text{.}5\right)$

## Probability distribution

Write the probability density function.

$f\left(x\right)$ $\phantom{\rule{0ex}{0ex}}=$ $\frac{1}{9}$

Graph the probability distribution.

• Sketch the graph of the probability distribution.
• Identify the following values:
• Lowest value for $x$ :
• Highest value for $x$ :
• Height of the rectangle:
• Label for x-axis (words):
• Label for y-axis (words):
• 0.5
• 9.5
• $\frac{1}{9}$
• Age of Cars
• $f\left(x\right)$

## Random probability

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

• Sketch the graph. Shade the area of interest.
• Find the probability. $P\left(x<\text{4}\right)$ =
• $\frac{3\text{.}5}{9}$

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.

• Sketch the graph. Shade the area of interest.
• Find the probability. $P\left(x<4\mid x<7\text{.}5\right)$ =
• $\frac{3\text{.}5}{7}$

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

## Quartiles

Find the average age of the cars in the lot.

$\mu$ = 5

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.

• Sketch the graph. Shade the area of interest.
• Find the value $k$ such that $P\left(x .
• The third quartile is:
• $k$ = 7.25

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