   Chapter 9.2, Problem 30E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

# Demand The daily demand for gasoline x (in millions of gallons) in a city is described by the probability density function f ( x ) = 0.41 − 0.08 x , [ 0 , 4 ] .Find the probability that the daily demand for gasoline will be (a) no more than 3 million gallons and (b) at least 2 million gallons.

(a)

To determine

To calculate: The probability if the daily demand for gasoline will not be more than 3 million gallons. If the total demand of a city for gasoline is represented by the probability density function as, f(x)=0.410.08x, [0,4] where x represents the number of gallon’s(in million).

Explanation

Given Information:

The total demand of a city for gasoline is represented by the probability density function as, f(x)=0.410.08x, [0,4] where x represents the number of gallon’s(in million).

Formula used:

If f is function of a continuous random variable x, then the probability that x lies in the interval [c,d] is,

P(cxd)=cdf(x) dx

Calculation:

Consider the provided probability density function,

f(x)=0.410.08x, [0,4]

Since, the daily demand for gasoline will not be more than 3 million gallons therefore,

The interval in which probability lies is 0x3.

Now, apply the formula of probability P(cxd)=cdf(x) dx.

Substitute the values 0 for c, 3 for d and 0.410.08x for f(x) in the above formula as,

P(0x3)=030

(b)

To determine

To calculate: The probability if the daily demand for gasoline will be at least 2 million gallons. If the total demand of a city for gasoline is represented by the probability density function as, f(x)=0.410.08x, [0,4] where x represents the number of gallon’s(in million).

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 