# 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. BuyFindarrow_forward ### Calculus: An Applied Approach (Min... 10th Edition Ron Larson Publisher: Cengage Learning ISBN: 9781305860919 #### Solutions Chapter Section BuyFindarrow_forward ### Calculus: An Applied Approach (Min... 10th Edition Ron Larson Publisher: Cengage Learning ISBN: 9781305860919 Chapter 9, Problem 17RE Textbook Problem 3 views ## 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) 0.1 0.2 0.5 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) 0.1 0.2 0.5 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) 0.1 0.2 0.5 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) 0.1 0.2 0.5 0.15 0.05

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