Question

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?

Answer 1

Using Chebychev's theorem,

We know that,

Minimum percentage of data within two Standard deviation is 75%.

Here,

92 is 2 times standard deviation above the mean.

Hence,

Half of the remaining (100-75)%= 25% data will lies above the 92.

i.e.,

Approximately, 12.5% of scores that are above 92.

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