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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 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):

Short Answer

Expert verified

a. The graph will be;

b.

b. Identify the following values:

i. Lowest value forx炉=0.5

ii. Highest value for x炉=9.5

iii. Height of the rectangle: role="math" localid="1648215909648" 19

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

v. Label for y-axis (words):19

Step by step solution

01

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

02

Probability Distribution Graph

Considering above scenario probability distribution function will be;

f(x)=1b-a=19.5-0.5=19

Thus the Probability distribution graph will be ;

03

Identification of values

b. Identify the following values:

i. Lowest value forx炉=0.5

ii. Highest value for x炉=9.5

iii. Height of the rectangle: role="math" localid="1648216112183" 19

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

v. Label for y-axis (words):19

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Most popular questions from this chapter

Suppose that the longevity of a light bulb is exponential with a mean lifetime of eight years.

a. Find the probability that a light bulb lasts less than one year.

b. Find the probability that a light bulb lasts between six and ten years.

c. Seventy percent of all light bulbs last at least how long?

d. A company decides to offer a warranty to give refunds to light bulbs whose lifetime is among the lowest two percent of all bulbs. To the nearest month, what should be the cutoff lifetime for the warranty to take place?

e. If a light bulb has lasted seven years, what is the probability that it falls within the 8th year.

What is the area under f(x) if the function is a continuous probability density function?

What is the probability that a phone will fail within two years of the date of purchase?

a.0.8647

b. 0.4866

c. 0.2212

d. 0.9997

Use the following information to answer the next eight exercises. A distribution is given as X~U(0,12).

Draw the graph of the distribution for P(x>9).

Suppose that the length of long distance phone calls, measured in minutes, is known to have an exponential distribution with the average length of a call equal to eight minutes.

a. Define the random variable. X=

b. Is X continuous or discrete?

c. X~

d. 渭=

e. 蟽=

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

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h. Find the probability that a phone call lasts more than nine minutes.

i. Find the probability that a phone call lasts between seven and nine minutes.

j. If 25 phone calls are made one after another, on average, what would you expect the total to be? Why?
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