Question 43 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
The difference in sample proportions, B − C, has mean 0.29 − 0.35 = −0.06 and standard error √[(0.29 × 0.71)/50 + (0.35 × 0.65)/50] ≈ 0.093. Becky’s proportion is greater when B − C > 0, which corresponds to z = [0 − (−0.06)]/0.093 ≈ 0.64. The area to the right of z = 0.64 is about 0.259, so the probability is 0.259.
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