Answer to Question #274005 in Statistics and Probability for nini

Question

The average age of bank managers is 35 years. Assume the variable is normally distributed. If the standard deviation is 5 years, find the probability that the age of a randomly selected bank manager will be in the range between 25 and 40 years old.

Answer 1

$P(25<X<40)=P(\frac{25-35}{5}<Z<\frac{40-35}{5})$

$=P(-2<Z<1)$

$=P(Z<1)-P(Z<-2)$

From normal standard distribution table;

$P(25<X<40)=0.8413-0.0227$

$P(25<X<40)=0.8186$