Question #337326

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?

1
Expert's answer
2022-05-06T11:19:01-0400
P(X<x1)=P(Z<x120020)=0.025P(X<x_1)=P(Z<\dfrac{x_1-200}{20})=0.025




x120020=1.96\dfrac{x_1-200}{20}=-1.96

x1=160.8x_1=160.8



P(X>x2)=1P(Zx220020)=0.025P(X>x_2)=1-P(Z\ge\dfrac{x_2-200}{20})=0.025





x220020=1.96\dfrac{x_2-200}{20}=1.96

x2=239.2x_2=239.2



160.8 and 239.2



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