7
QuizMultiple Choice

Combining Two Random Variables

Question 7 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)

Lynnetta gets paid weekly for completing household chores. The amount of money she earns for doing dishes, D, is approximately Normally distributed with a mean of $53 and a standard deviation of $3.60. The amount of money she earns for doing laundry, L, is approximately Normally distributed with a mean of $47 and a standard deviation of $4.10. Assume that D and L are independent random variables.What is the probability that Lynnetta will earn more than $110 in a randomly selected week?

Answer
A
0.034
B
0.097
C
0.249
D
0.966

Explanation

Because the earnings are independent, the total weekly earnings have mean $53 + $47 = $100 and standard deviation √(3.60² + 4.10²) ≈ $5.46. A total of $110 is about (110 − 100) / 5.46 ≈ 1.83 standard deviations above the mean. The probability of earning more than that is about 0.034, so the correct choice is A, 0.034.

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