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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.

Write the probability density function

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$\stackrel{¯}{x}=$

ii. Highest value for localid="1648215651207" $\stackrel{¯}{x}=$

iii. Height of the rectangle:

iv. Label for x-axis (words):

v. Label for y-axis (words):

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. Find the average age of the cars in the lot.

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.

Considering only the cars less than 7.5 years old, find the probability that a randomly chosen car in the lot was less than four years old.

a. Sketch the graph, shade the area of interest.

b. Find the probability$P(x<\overline{)4}x<7.5)=$

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.

Find the third quartile of ages of cars in the lot. This means you will have to find the value such that $\frac{3}{4}or75\%$,of the cars are at most (less than or equal to) that age.

a. Sketch the graph, and shade the area of interest.

b. Find the value k such that$P(x<K)=0.75$

c. The third quartile is _____

Use the following information to answer the next ten exercises. A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution: $X~Exp(0.2)$

What type of distribution is this?

Use the following information to answer the next ten exercises. A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution: $X~Exp(0.2)$

What is the mean?

Consider the function $f\left(x\right)=\frac{1}{8}$ for $0≤x≤8$. Draw the graph of $f\left(x\right)$ and find $P(2.5<x<7.5)$.

Suppose that the distance, in miles, that people are willing to commute to work is an exponential random variable with a decay parameter $\frac{1}{20}$. Let X = the distance people are willing to commute in miles. What is m, μ, and σ? What is the probability that a person is willing to commute more than 25 miles?

$f\left(x\right)$for a continuous probability function is$15$ , and the function is restricted to $0≤x≤5$. What is $P(x<0)$?