15
QuizMultiple Choice

Unit Test — Unit test

Question 15 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)

In bags of Happy Trail Mix, the number of raisins is skewed left with a mean of 33.6 and a standard deviation of 8.4, while in bags of a generic trail mix, the number of raisins is skewed right with a mean of 28.8 and a standard deviation of 12.7. What is the probability in a sample of 17 randomly selected Happy Trail Mix bags and a sample of 17 randomly selected generic bags that the mean number of raisins in the Happy Trail Mix is more than the mean number of raisins in the generic mix?

Answer
A
approximately 0
B
0.0968
C
0.8219
D
0.9032

Explanation

The difference between the sample means has expected value 33.6 − 28.8 = 4.8 raisins and standard error √(8.4²/17 + 12.7²/17) ≈ 3.69. Using the normal approximation for the difference, the probability that this difference is greater than 0 is Φ(4.8/3.69) = Φ(1.30) ≈ 0.9032. Thus the probability is approximately 0.9032.

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