5.5 Practice 1: uniform distribution

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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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