SOLUTION: A statistics teacher believes that the final exam grades for her elementary statistics class have a normal distribution with a mean of 82 and a standard deviation of 8.
a. Find th
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Question 835668: A statistics teacher believes that the final exam grades for her elementary statistics class have a normal distribution with a mean of 82 and a standard deviation of 8.
a. Find the score which separates the top 10% of the scores from the lowest 90% of the scores.
b. 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.
c. Find the score which separates the lowest 20% of the scores from the highest 80% of the scores.
d. The teacher plans to give all students who scores in the lowers 10% of scores an F. will a student who scored 65 on the exam receive F? Explain
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A statistics teacher believes that the final exam grades for her elementary statistics class have a normal distribution with a mean of 82 and a standard deviation of 8.
a. Find the score which separates the top 10% of the scores from the lowest 90% of the scores.
Find the z-value with a right tail of 10%
invNorm(0.90) = 1.2816
Find the corresponding raw score::
x = 1.2816*8+82 = 92.25
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b. 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.
Ans: No; the student needs a score of at leasst 92.25
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c. Find the score which separates the lowest 20% of the scores from the highest 80% of the scores.
z-score for left-tail of 20% = invNorm(0.20) = -0.8416
x = -0.8416*8+82 = 75.27
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d. The teacher plans to give all students who scores in the lowers 10% of scores an F. will a student who scored 65 on the exam receive F? Explain
z-score = invNorm(0.10) = -1.2816
Top score in lower 10% = -1.2816*8+82 = 71.74
A student with a 65 would get an F because 65 < 71.74
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Cheers,
Stan H.
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