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Collaborative statistics Continuous random variables Practice 1: uniform distribution
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
Probability distribution
Graph the probability distribution.
a Sketch the graph of the probability distribution.
b Identify the following values:
i Lowest value for
x
size 12{X} {} :
ii Highest value for
x
size 12{X} {} :
iii Height of the rectangle:
iv Label for x-axis (words):
v Label for y-axis (words):
b.i 0.5
b.ii 9.5
b.iii
1
9
size 12{ { {1} over {9} } } {}
b.iv Age of Cars
b.v
f
(
x
)
size 12{f \( x \) } {} Got questions? Get instant answers now!
Random probability
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.
P
(
x
<
4
)
size 12{P \( X<"5730" \) } {} =
b.
3
.
5
9
size 12{ { {3 "." 5} over {9} } } {} Got questions? Get instant answers now!
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.
P
(
x
<
4
∣
x
<
7
.
5
)
size 12{P \( X<4 \lline X<7 "." 5 \) } {} =
b
3
.
5
7
size 12{ { {3 "." 5} over {7} } } {} Got questions? Get instant answers now!
Quartiles
Find the third quartile of ages of cars in the lot. This means you will have to find the value such that
3
4
size 12{ { {3} over {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
size 12{k} {} such that
P
(
x
<
k
)
=
0
.
75
size 12{P \( X<k \) =0 "." "75"} {} .
c The third quartile is:
Got questions? Get instant answers now!
Source:
OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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