The average age of a manager is 58 years old if you assume t

The average age of a manager is 58 years old. if you assume that the age variable is normally distributed and has a standard deviation of 3.2 years, what is the probability that the age of a randomly selected manager will be between 51 to 56 years old?

Solution

b) 51<= P=> 56 years

x=51 z= (51 – 58 )/( 3.2) =-2.19 so the probability P=>-2.19 is = 0.0143

x=56 z= (56 – 58 )/( 3.2) =-0.625 so the probability P=>-0.63 is = 0.2643

so the probability (51<= P=> 56)=0.2643-0.0143 =0.25, take into account the probability of positive Z to right wing and if the number is negative to the left