Question

The average IQ score on a certain campus is 110. If the variance of these scores is 15, what can be said about the percentage of students with an IQ above 140? Hint: Use Chebyshev’s inequality.

Answer 1

The average IQ score on a certain campus is 110. The variance of these scores is 15.

We have to conclude about the percentage of students, with an IQ above 140.

Now, we know that Chebyshev's one tailed inequality states that

Where, X is a random variable with mean and variance ; and k>0.

Now, here X has mean 110 and variance 15.

We have to find

=

=

=

Now, 110 is the mean, and square root of 15 is standard deviation.

=

So, here k is 7.746.

So, the upper bound to the probability is

=

=

=

So, the corresponding upper bound of the percentage is 0.0164*100, ie. 1.64%.

So, the percentage of students with an IQ above 140, has an upper bound of 1.64%.