Chapter 5: Q.40 (page 349)

Use the following information to answer the next eleven exercises. 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.
a. Graph the probability distribution
b. Identify the following values:
i. Lowest value for $\bar{x} =$
ii. Highest value for localid="1648215651207" $\bar{x} =$
iii. Height of the rectangle:
iv. Label for x-axis (words):
v. Label for y-axis (words):

Short Answer

Expert verified

a. The graph will be;

b. Identify the following values:

i. Lowest value for $\bar{x} = 0.5$

ii. Highest value for $\bar{x} = 9.5$

iii. Height of the rectangle: role="math" localid="1648215909648" $\frac{1}{9}$

iv. Label for x-axis (words):role="math" localid="1648216082037" $0.5 < x < 9.5$

v. Label for y-axis (words): $\frac{1}{9}$

Step by step solution

Scenario analysis

According to the given scenario;

The age of cars in staff parking lot of suburban college; those are considered to be uniformly distributed.

Let consider;

The age of the cars in suburban college is denoted with X, hence x can be considered as intervals.

Thus; $= 0.5 < x < 9.5$

Probability Distribution Graph

Considering above scenario probability distribution function will be;

$\begin{array}{rcl} f (x) & = & \frac{1}{b - a} \\ = & \frac{1}{9.5 - 0.5} \\ = & \frac{1}{9} \end{array}$

Thus the Probability distribution graph will be ;

Identification of values

b. Identify the following values:

i. Lowest value for $\bar{x} = 0.5$

ii. Highest value for $\bar{x} = 9.5$

iii. Height of the rectangle: role="math" localid="1648216112183" $\frac{1}{9}$

iv. Label for x-axis (words): $0.5 < x < 9.5$

v. Label for y-axis (words): $\frac{1}{9}$

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Short Answer

Step by step solution

Scenario analysis

Probability Distribution Graph

Identification of values

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