A civil service exam yields scores with a mean of 81 and a standard deviation of 5.5. Using Chebyshev's Theorem what can we say about the percentage of scores that are above 92?
Select one:
A. At most 12.5% of the scores are above 92.
B. At most 25% of the scores are above 92.
C. At least 75% of the scores are above 92.
D. At least 25% of the scores are above 92.
E. None of the above
Solution:
Given: A civil service exam yields scores with a mean of 81 and a standard deviation of 5.5.
Thus mean = and standard deviation =
We have to find the percentage of scores that are above 92 using Chebyshev's Theorem.
According to Chebyshev’s inequality, at most of the data fall outside k standard deviation from mean.
Thus find k:
92 is above 81 so use:
Thus 92 is 2 standard deviation above mean.
Thus find:
At most 25% data fall outside 2 standard deviation , that is : below 2 standard deviation and above 2 standard deviation, but we have to find only % of data above 2 standard deviation, thus half of 25% = 12.5%
Thus correct option is:
A. At most 12.5% of the scores are above 92.
A civil service exam yields scores with a mean of 81 and a standard deviation of...
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