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

View Explanation

Log in for full answers

Similar Questions

For a normal distribution, which of the following z−scores represents the most extreme location on the left side of the distribution?

For a standardized normal distribution, determine a value, say z0, so that P(z > z0) = 0.025.

Suppose X is a random variable with a normal distribution with mean mu and standard deviation sigma. What is the value of z that makes this a true statement? ( Find Z that satisfies this equation ) 𝑃 ( − 𝑧 < 𝑋 − 𝜇 𝜎 < 𝑧 ) = .96 Draw picture and label it.

Suppose X is a random variable with a normal distribution with mean mu and standard deviation sigma. What is the value of z that makes this a true statement? ( Find Z that satisfies this equation ) 𝑃 ( − 𝑧 < 𝑋 − 𝜇 𝜎 < 𝑧 ) = .90 Draw picture and label it.

Question at position 12 Scores on Dr. Bond's test have a mean of 70 and a standard deviation of 11. Michelle has a score of 48. Convert Michelle's score to a z-score. (Round to two decimal places if necessary.)41.641.33-22Clear my selection

Assuming values are normally distributed, which of the following data points is the most extreme value:

Suppose X is a random variable with a normal distribution with mean mu and standard deviation sigma. What is the value of z that makes this a true statement? ( Find Z that satisfies this equation ) 𝑃 ( − 𝑧 < 𝑋 − 𝜇 𝜎 < 𝑧 ) = .96 Draw picture and label it.

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler