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Revenue A publishing company introduces a new weekly magazine that sells for $3.95. The marketing group of the company estimates that the sales x (in thousands) will be approximated by the following probability function. x 10 15 20 30 40 P ( x ) 0.10 0.20 0.50 0.15 0.05 Find E ( x ) and σ. Find the expected revenue.

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919
Chapter 9, Problem 17RE
Textbook Problem
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Revenue A publishing company introduces a new weekly magazine that sells for $3.95. The marketing group of the company estimates that the sales x (in thousands) will be approximated by the following probability function.

x 10 15 20 30 40
P(x) 0.10 0.20 0.50 0.15 0.05

Find E(x) and σ.

Find the expected revenue.

(a)

To determine

To calculate: The expected value E(x) and standard deviation σ of the probability function of a publishing company:

x

10

15

20

30

40

P(x)

0.10

0.20

0.50

0.15

0.05

Explanation of Solution

Given Information:

A new weekly magazine is sold for $3.95 which was introduced by a publishing company. The sales x (in thousands) is estimated to be approximated by the probability function:

x

10

15

20

30

40

P(x)

0.10

0.20

0.50

0.15

0.05

Formula used:

If a discrete random variable takes the values {x1,x2,,xm}, then the expected value of the random variable is defined as,

E(x)=x1P(x1)+x2P(x2)++xmP(xm)

Variance of the random variable is defined as,

V(x)=(x1μ)2P(x1)+(x2μ)2P(x2)++(xmμ)2P(xm)

The standard deviation of the random variable is defined as,

σ=V(x)

Calculation:

Consider a new weekly magazine which is sold for $3.95 introduced by a publishing company. The sales x (in thousands) is estimated to be approximated by the probability function:

x

10

15

20

30

40

P(x)

0.10

0.20

0.50

0.15

0.05

First use the provided probability function and the expected value formula E(x)=x1P(x1)+x2P(x2)++xmP(xm) to calculate the expected value of the probability distribution

(b)

To determine

To calculate: The expected revenue of the probability function of a publishing company which introduces a new weekly magazine sold for $3.95.

x

10

15

20

30

40

P(x)

0.10

0.20

0.50

0.15

0.05

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Chapter 9 Solutions

Calculus: An Applied Approach (MindTap Course List)
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