Question

Suppose that IQ scores have a bell-shaped distribution with a mean of 103 and a standard deviation of 15. Using the empirical rule, what percentage of IQ scores are at least 58? Please do not round your answer.

Answer 1

Probability = 0.15%

Explanation:

The provided information is:

Let X be the scores of the IQ scores that is normally distributed with mean
`\mu = 103` and standard deviation

.

That is
`X \sim N(103,15)`

`103 - 58 = 45 = 3 * 15`

So, 58 is 3 standard deviation left to the mean.

As 99.7% of probability lies within the three standard deviation.

Thus, above three standard deviation is:

`(1-0.997)/(2)=0.0015`

Thus, the required probability is 0.15%