AnswersEHS Content Recovery - Probability and Statistics - Part CCalculating Probabilities for Sampling DistributionQuestion 10
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Calculating Probabilities for Sampling Distribution

Question 10 • EHS Content Recovery - Probability and Statistics - Part C

Carol and Diane are axe throwers. Carol hits the board on 44% of her throws, while Diane hits the board on 42% of her throws. Suppose that Carol throws 25 axes at the board and Diane throws 28. Let C = the proportion of axes that hit the board when Carol throws and D = the proportion of axes that hit the board when Diane throws. What is the probability that Diane’s proportion of axes hitting the board is higher than Carol’s?Find the z-table here.

Answer
A
0.442
B
0.456
C
0.491
D
0.558

Explanation

The difference D − C has mean 0.42 − 0.44 = −0.02 and standard deviation √[(0.42 × 0.58)/28 + (0.44 × 0.56)/25] ≈ 0.136. The z-score for D − C = 0 is (0 − (−0.02))/0.136 ≈ 0.15. The probability that D − C is above zero is about 0.442, so the answer is A, 0.442.

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