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

Answer:

Probability = 0.15%

Step-by-step 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  $X \sim N(103,15)$

$103 - 58 = 45 = 3 \times 15$

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:

$\frac{1-0.997}{2}=0.0015$

Thus, the required probability is 0.15%