Answer to Question #337326 in Statistics and Probability for Jeve Quinones

Question

A normally distributed data has a mean of 200 and a standard deviation of 20.What are the two extreme scores, outside of which only 5% of the distribution are expected to fall?

Answer 1

$$P(X<x_1)=P(Z<\dfrac{x_1-200}{20})=0.025$$

$$\dfrac{x_1-200}{20}=-1.96$$

$$x_1=160.8$$

$$P(X>x_2)=1-P(Z\ge\dfrac{x_2-200}{20})=0.025$$

$$\dfrac{x_2-200}{20}=1.96$$

$$x_2=239.2$$

160.8 and 239.2