Question

Suppose that IQ scores have a bell-shaped distribution with a mean of 103 and a standard deviation of 14. Using the empirical rule, what percentage of IQ scores are between 61 and 145

Answer 1

Answer:

$P(61<x<145)$

And we can use the z score formula in order to find the deviationn above/below for the limits given given by:

$z= \frac{X -\mu}{\sigma}$

And replacing we got:

$z=\frac{61-103}{14}= -3$

$z=\frac{145-103}{14}= 3$

So then we want the % of values within 3 deviation from the mean and from the empirical rule we know that between these we have 99.7% of the data.

Step-by-step explanation:

We know that the IQ scores have the following parameters:

$\mu = 103, \sigma = 14$

And we want to find the following probability:

$P(61<x<145)$

And we can use the z score formula in order to find the deviationn above/below for the limits given given by:

$z= \frac{X -\mu}{\sigma}$

And replacing we got:

$z=\frac{61-103}{14}= -3$

$z=\frac{145-103}{14}= 3$

So then we want the % of values within 3 deviation from the mean and from the empirical rule we know that between these we have 99.7% of the data.