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Chapter 5: Question 85 (page 355)

The number of miles driven by a truck driver falls between 300and700, and follows a uniform distribution.

a. Find the probability that the truck driver goes more than 650miles in a day.

b. Find the probability that the truck drivers goes between 400and650miles in a day.

c. At least how many miles does the truck driver travel on the furthest 10%of days?

Short Answer

Expert verified

a) The probability that the truck driver goes more than 650miles in a day is 0.125.

b) The probability that the truck drivers goes between 400and650miles in a day is 0.625

c) The truck driver travels at least 660miles on the furthest 10%of days

Step by step solution

01

Defining the height of Probability distribution

It is given that X~U(300,700)

Therefore, the height or probability distribution of the data will be:

f(x)=1b-a=1700-300=1400

02

Finding the probability that the truck driver goes more than 650 miles in a day.

a) The required probability can be calculated as below:

P(x>650)=base脳height=(700-650)脳1400=50400=0.125

03

Finding the probability that the truck drivers goes between 400 and 650 miles in a day.

b) The required probability can be calculated as below:

P(400<x<650)=base脳height=(650-400)脳1400=250400=0.625
04

 Step 4 : Finding at least how many miles does the truck driver travel on the furthest 10% of days?

c) The required 10thpercentile can be calculated as below:

P(x>k)=base脳height鈬�0.10=(700-k)脳1400鈬�400脳0.10=700-k鈬�k=660

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