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Chapter 5: Q.45 (page 350)

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 34or75%,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 thatP(x<K)=0.75

c. The third quartile is _____

Short Answer

Expert verified

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

b. Value of K = 7.25

c. The third quartile is 7.25

Step by step solution

01

Scenario Description

Here in the problem

Uniform distribution has been considered within the age of cars in staff parking lot of suburban college

Here in problem the age of the cars in suburban college is represented with X, and x as intervals.

Therefore; 0.5<x<9.5

Here a=0.5b=9.5

Hence; fx=1b-a=19

02

Step Representation of Graph

The graph of the third percentile will be as follows;

03

Value of K

The value of K for Third percentile will be as follows;

P(x<k)=Base脳Height0.75=k-0.5脳19k=(9脳0.75)+0.5=7.25

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Most popular questions from this chapter

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 forx炉=

ii. Highest value for localid="1648215651207" x炉=

iii. Height of the rectangle:

iv. Label for x-axis (words):

v. Label for y-axis (words):

A distribution is given as X~U(0,20). What is P(2<x<18)? Find the90thpercentile.

The cost of all maintenance for a car during its first year is approximately exponentially distributed with a mean of \(150.

a. Define the random variable.X=_________________________________.

b.X~=________

c.渭=________

d.蟽=________

e. Draw a graph of the probability distribution. Label the axes.

f. Find the probability that a car required over \)300for maintenance during its first year.

At an urgent care facility, patients arrive at an average rate of one patient every seven minutes. Assume that the duration between arrivals is exponentially distributed.

a. Find the probability that the time between two successive visits to the urgent care facility is less than \(2\) minutes.

b. Find the probability that the time between two successive visits to the urgent care facility is more than \(15\) minutes.

c. If \(10\) minutes have passed since the last arrival, what is the probability that the next person will arrive within the

next five minutes?

Use the following information to answer the next three exercises.

The Sky Train from the terminal to the rental鈥揷ar and long鈥搕erm parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution.

The probability of waiting more than seven minutes given a person has waited more than four minutes is?

a. 0.125

b. 0.25

c. 0.5

d. 0.75
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