Question

In: Statistics and Probability

A statistics teacher believes that the final exam grades for her business statistics class have a...

A statistics teacher believes that the final exam grades for her business statistics class have a normal distribution with a mean of 82 and a standard deviation of 8.

(1)Find the score which separates the top 10% of the scores from the lowest 90% of the scores.

(2)

The teacher plans to give all students who score in the top 10% of scores an A. Will a student who scored a 90 on the exam receive an A? Explain.

(3)

Find the score which separates the lowest 20% of the scores from the highest 80% of the scores.
(4)

The teacher plans to give all students who score in the lowest 10% of score an F. Will a student who scored a 65 on the exam receive an F? Explain.

Solutions

Expert Solution

Answer:

Given that:

A statistics teacher believes that the final exam grades for her business statistics class have a normal distribution with a mean of 82 and a standard deviation of 8.

We are given

Mean = 82

SD = 8

1) Find the score which separates the top 10% of the scores from the lowest 90% of the scores.

Z score for top 10% = 1.281552

(by using z-table)

X = Mean + Z*SD

X = 82 + 1.281552*8

X = 92.25242

Required score = 92.25242

2) The teacher plans to give all students who score in the top 10% of scores an A. Will a student who scored a 90 on the exam receive an A? Explain.

Answer: A student who scored a 90 on the exam will not receive an A because it is less than 92.25242.

3) Find the score which separates the lowest 20% of the scores from the highest 80% of the scores.

Z score for lowest 20% = -0.84162

(by using z-table)

X = Mean + Z*SD

X = 82 + (-0.84162)*8

X = 75.26704

Required score = 75.26704

4) The teacher plans to give all students who score in the lowest 10% of score an F. Will a student who scored a 65 on the exam receive an F? Explain.

Z score for lowest 10% = -1.28155

(by using z-table)

X = Mean + Z*SD

X = 82 + (-1.28155)*8

X = 71.7476

Required score =71.7476

A student who scored a 65 on the exam will receive an F because the score 65 is less than 71.7476.


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