A filling station is supplied with gasoline once a week. If its weekly volume of

tapetivk

tapetivk

Answered question

2021-11-13

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(1x)40<x<10otherwise 
what must the capacity of the tank be so that the probability of the supply’s being exhausted in a given week is .01?

Answer & Explanation

Ryan Willis

Ryan Willis

Beginner2021-11-14Added 15 answers

Given the weekly volume of sales is a random variable, say X with density as
f(x)={5(1x)40<x<10otherwise
Let c be the capacity of the tank.
Given that the probability that sales will exceed the capacity in a given week is 0.01, we have
P[X>c]=0.01
cf(x)dx=0.01
c15(1x)4dx=0.01
[5(1x)55]c1=0.01
[(1x)5]c1=0.01
(1c)5=0.01
1c=(0.01)15
1c=0.398
c=10.398
c=0.602
Thus, capacity of the tank is 0.6 thousands of gallons
Result
Capacity of the tank is 0.6 thousands of gallons

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