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DanielleElmas [232]
2 years ago
7

Iq scores are normally distributed with a mean of 100 and a standard deviation of 15.

Mathematics
1 answer:
bearhunter [10]2 years ago
6 0

Mean is \mu=100 and a standard deviation is \sigma =15, then the variable X\sim N(100,15^2).

Use substitution

Z=\dfrac{X-\mu}{\sigma},\\  \\ Z=\dfrac{X-100}{15}.

This substitution gives you that Z\sim N(0,1).

a. For X=130, Z=\dfrac{130-100}{15}=2 and Pr(X>130)=Pr(Z>2) =0.9772 (the decimal value is taken from the Standard Normal Distribution Table).

b. For X=90, Z=\dfrac{90-100}{15}=-\dfrac{2}{3} and for X=110, Z=\dfrac{110-100}{15}=\dfrac{2}{3}. Then Pr(90 (the decimal value is taken from the Standard Normal Distribution Table).

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