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?
Seamus
4.998 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
Step 2: Use the formula for the expected value (mean) which is given by:
Step 3: Calculate the weighted sum of the donations:
Step 4: Compute each term:
Step 5: Sum the results:
Therefore, the average donation received per person at this business is:
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