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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

Respuesta :

Answer:

[tex] P(61<x<145)[/tex]

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

[tex] z= \frac{X -\mu}{\sigma}[/tex]

And replacing we got:

[tex] z=\frac{61-103}{14}= -3[/tex]

[tex] z=\frac{145-103}{14}= 3[/tex]

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:

[tex]\mu = 103, \sigma = 14[/tex]

And we want to find the following probability:

[tex] P(61<x<145)[/tex]

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

[tex] z= \frac{X -\mu}{\sigma}[/tex]

And replacing we got:

[tex] z=\frac{61-103}{14}= -3[/tex]

[tex] z=\frac{145-103}{14}= 3[/tex]

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.

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