Question

Donations are accepted at a local business. The dollar amounts, and probability that a person donates that amount is given in the table below: Donation (x) P(x) 5 .05 10 .21 15 .22 20 .20 25 .15 30 .11 35 .06 What is the average donation received per person at this business?

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Answer to a math question Donations are accepted at a local business. The dollar amounts, and probability that a person donates that amount is given in the table below: Donation (x) P(x) 5 .05 10 .21 15 .22 20 .20 25 .15 30 .11 35 .06 What is the average donation received per person at this business?

$Expert avatar$

Seamus

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98 Answers

Step 1: Identify the dollar amounts (x) and corresponding probabilities (P(x)).

Step 2: Use the formula for the expected value (mean) which is given by:

E(X) = \sum (x \cdot P(x))

Step 3: Calculate the weighted sum of the donations:

E(X) = 5 \cdot 0.05 + 10 \cdot 0.21 + 15 \cdot 0.22 + 20 \cdot 0.20 + 25 \cdot 0.15 + 30 \cdot 0.11 + 35 \cdot 0.06

Step 4: Compute each term:

5 \cdot 0.05 = 0.25

10 \cdot 0.21 = 2.1

15 \cdot 0.22 = 3.3

20 \cdot 0.20 = 4.0

25 \cdot 0.15 = 3.75

30 \cdot 0.11 = 3.3

35 \cdot 0.06 = 2.1

Step 5: Sum the results:

0.25+2.1+3.3+4.0+3.75+3.3+2.1=18.8

Therefore, the average donation received per person at this business is:

E(X)=18.8

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