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Problem 10

# The owner of a newsstand in a college community estimates the weekly demand for a certain magazine as follows: $$\begin{array}{lcccccc} \hline \text { Quantity } & & & & & & \\ \text { Demanded } & 10 & 11 & 12 & 13 & 14 & 15 \\ \hline \text { Probability } & .05 & .15 & .25 & .30 & .20 & .05 \\ \hline \end{array}$$ Find the number of issues of the magazine that the newsstand owner can expect to sell per week.

Expert verified
The expected weekly demand for the magazine is approximately 10.6 issues, which means the newsstand owner can plan to sell about 11 issues of the magazine per week.
See the step by step solution

## Step 1: Identify the variables and probabilities

We are given the following information: Quantities Demanded (X): 10, 11, 12, 13, 14, 15 Probabilities (P(X)): .05, .15, .25, .30, .20, .05

## Step 2: Calculate the Expected Value

The expected value (E(X)) is calculated using the formula: E(X) = Σ[X * P(X)], where X is the quantity demanded and P(X) is the probability of that quantity being demanded. E(X) = (10 * .05) + (11 * .15) + (12 * .25) + (13 * .30) + (14 * .20) + (15 * .05)

## Step 3: Compute the sum

Calculate the sum using the given values: E(X) = 0.5 + 1.65 + 3.0 + 3.9 + 2.8 + 0.75

## Step 4: Calculate the expected value

Now, simply add the results of each term to find the total expected value: E(X) = 0.5 + 1.65 + 3.0 + 3.9 + 2.8 + 0.75 = 10.6 The newsstand owner can expect to sell about 10.6 issues of the magazine per week. Since selling a fraction of a magazine is not possible, the newsstand owner can use this expected value as an approximation and plan to sell about 11 issues of the magazine per week.

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