Question at position 45 CBAED

Question

BlackTom AI · Accepted Answer

First, I’ll restate the problem setup and the answer choices to ensure clarity.
- Jack and Jill have mean scores and standard deviations: Jack mean 12,400 with SD 1,500; Jill mean 14,200 with SD 2,000. They each play once, and their z-scores are compared.
- Jack scores 14,000; Jill scores 16,000.
- Answer choices are labeled A through E.

Now I’ll evaluate each option to see what the z-scores actually are and who wins.
Option A: Jack’s z = 1.07, Jill’s z = 1.11, Jill wins the contest.
- Calculation for Jack: z = (14,000 − 12,400) / 1,500 = 1,600 / 1,500 ≈ 1.07. This part is correct. 
- Calculation for Jill: z = (16,000 − 14,200) / 2,000 = 1,800 / 2,000 = 0.90, not 1.11. So this option misstates Jill’s z and also incorrectly states Jill wins.

Option B: Jack’s z = 1.07, Jill’s z = 0.90, Jack wins the contest.
- Jack’s z calculation is exactly 1.07 as above.
- Jill’s z calculation is (16,000 − 14,200) / 2,000 = 1,800 / 2,000 = 0.90, matching this option.
- Since Jack’s z is higher than Jill’s, Jack has the higher relative standing and thus wins. This option is internally consistent and correct.

Option C: Jack’s z = 0.94, Jill’s z = 1.11, Jill wins the contest.
- Jack’s z would be (14,000 − 12,400) / 1,500 = 1.07, not 0.94. This is an incorrect computation for Jack’s z.
- Jill’s z again incorrectly states 1.11, which is not consistent with the given numbers. Even if Jill’s z were correct, Jill would be the winner since 1.11 > 0.94, but due to wrong z-values, this option is invalid.

Option D: Jack’s z = 0.94, Jill’s z = 0.90, Jack wins the contest.
- Both z-values are miscalculated: Jack’s should be 1.07, not 0.94; Jill’s is correctly 0.90, but the pair together do not match the data. Moreover, even if Jack were 0.94, he would still have a lower z than Jill’s 0.90, so the winner would not be clear. This option is inconsistent with the actual z-scores.

Option E: Jack’s z = 0.81, Jill’s z = 0.99, Jill wins the contest.
- These z-values do not align with any of the proper computations: Jack’s z is not 0.81 (it’s 1.07), and Jill’s is not 0.99 (it’s 0.90). Additionally, Jill would win only if her z were higher than Jack’s, which would require Jill’s z to exceed 1.07, not 0.99. Therefore, this option is incorrect.

Through these checks, the only option that matches the correct z-scores and the correct winner is Option B, since Jack’s z is 1.07, Jill’s z is 0.90, and Jack wins the contest. The other options either misstate one or both z-scores or draw an incorrect conclusion about who wins based on faulty calculations.

Question at position 45 CBAED

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