- The student will explore the properties of data with a uniform distribution.
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.
What is being measured here?
The age of cars in the staff parking lot
In words, define the Random Variable
X
X
size 12{X} {}
.
X
X
size 12{X} {}
= The age (in years) of cars in the staff parking lot
Are the data discrete or continuous?
The interval of values for
X
X
size 12{X} {}
is:
The distribution for
X
X
size 12{X} {}
is:
X
X
size 12{X} {}
~
U
(
0
.
5,9
.
5
)
U
(
0
.
5,9
.
5
)
size 12{U \( 0 "." 5,9 "." 5 \) } {}
Write the probability density function.
f
(
x
)
f
(
x
)
size 12{f \( x \) } {}
=
=
1
9
1
9
size 12{ { {1} over {9} } } {}
Graph the probability distribution.
- a. Sketch the graph of the probability distribution.
- b. Identify the following values:
- i. Lowest value for
X
X
size 12{X} {}
:
- ii. Highest value for
X
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. Age of Cars
- b.iv.
1
9
1
9
size 12{ { {1} over {9} } } {}
- b.v.
f
(
x
)
f
(
x
)
size 12{f \( x \) } {}
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
)
P
(
X
<
4
)
size 12{P \( X<"5730" \) } {}
=
- b. -
3
.
5
9
3
.
5
9
size 12{ { {3 "." 5} over {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.
- a. Sketch the graph. Shade the area of interest.
- b. Find the probability.
P
(
X
<
4
∣
X
<
7
.
5
)
P
(
X
<
4
∣
X
<
7
.
5
)
size 12{P \( X<4 \lline X<7 "." 5 \) } {}
=
- b -
3
.
5
7
3
.
5
7
size 12{ { {3 "." 5} over {7} } } {}
Discussion Question
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
3
4
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
k
size 12{k} {}
such that
P
(
X
<
k
)
=
0
.
75
P
(
X
<
k
)
=
0
.
75
size 12{P \( X<k \) =0 "." "75"} {}
.
- c. The third quartile is:
- b.
k
k
size 12{k} {}
= 7.25
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