Question

let x be a continuous variable that is normally distributed with a mean of 25 and standard deviation of 4. find the area between x=18 and x=34

Answer 1

let x be a continuous variable that is normally distributed with a mean of 25 and standard deviation of 4. find the area between x=18 and x=34.

z=(X-μ)/ σ

for X=18. z=(18-25)/4=-1.75

for X=34. z=(34-25)/4=2.25

from a standard normal table:

p(z<2.25)=0.98778, p(z<-1.75)=0.04006

p(18<X<34)=p(-1.75<z<2.25)=p(z<2.25)-p(z<-1.75)=0.98778-0.04006=0.94772