AnswersCA-Statistics and Probability BUsing the Central Limit TheoremQuestion 10
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Using the Central Limit Theorem

Question 10 • CA-Statistics and Probability B

Libby earns a mean of 92.9 points with a standard deviation of 5.5 points in her math classes and a mean of 90.3 with a standard deviation of 6.1 points in her history classes. Both distributions are skewed left. If a sample of 30 of her math scores and 31 of her history scores is randomly selected, what is the probability that her mean math score will be more than her mean history score?

Answer
A
0.0401
B
0.0686
C
0.9314
D
0.9599

Explanation

The difference between the sample means, math minus history, has mean 92.9 − 90.3 = 2.6 points and standard error √(5.5²/30 + 6.1²/31) ≈ 1.486 points. Its z-score for a difference of 0 is (0 − 2.6)/1.486 ≈ −1.75. Therefore, the probability that the math sample mean is greater is P(Z > −1.75) ≈ 0.9599, choice D.

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