In: Statistics and Probability
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.
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.