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