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Chapter 5: Q.5.5 (page 212)

A filling station is supplied with gasoline once a week. If its weekly volume of sales in thousands of gallons is a random variable with probability density function

f(x)=5(1鈭�x)40<x<10otherwise

what must the capacity of the tank be so that the probability of the supply being exhausted in a given week is role="math" localid="1646634562935" .01?

Short Answer

Expert verified

the capacity of the tankc=0.602

Step by step solution

01

 Given Information.

f(x)=5(1鈭�x)40<x<10otherwise

02

Explanation.

c鈬�p(x>c)=0.07

role="math" localid="1646635699895" 鈭�c15(1-x)4dx=0.01

-5(1-x)55c1=0.07

03

Explanation.

1-c=(0.01)15

c=(1-0.01)15

=0.602

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