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According to psychologist IQs are normally distributed with a mean of 100 and a standard deviation of 19. What’s the percentage of the population has IQs above 154?

Sagot :

In order to solve this problem, we will calculate the z-score of the given data.

To do this, we use the formula,

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

We plug in the given data:

[tex]z=\frac{154-100}{19}\approx2.8421[/tex]

With this z-score, we can consult a z-score probability table or use an online resource. However, this will give us

[tex]P(z<2.8421)[/tex]

but we are interested in itbeing greater than it, so we must calculate

[tex]1-P(z<2.8421)=1-0.99776=0.00224[/tex]

So, the percentage of the population that has an IQ above 154 is 0.224%.

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