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

`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= (X -\mu)/(\sigma)`

And replacing we got:

`z=(61-103)/(14)= -3`

`z=(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.

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= (X -\mu)/(\sigma)`

And replacing we got:

`z=(61-103)/(14)= -3`

`z=(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.