Answer to Question #324274 in Statistics and Probability for Ivan

Question

In a beauty contest, the ages of the contestants are normally distributed with a mean of

24 years and a standard deviation of 1.5. What percent of the contestants have age

between 22.5 and 27 years old?

Answer 1

$P(22.5<x<27)=P(\frac{22.5-24}{1.5}<z<\frac{27-24}{1.5})\\ =P(-1<z<2)\\ =P(0<z<1)+P(0<z<2)\\ =0.3413+0.4772=0.8185\\ the\; percentage\; is\;81.85\%$