Question

5. The average age of Chief police is 56 years. Assume the variable is normally distributed. If the standard deviation is four years, find the probability that the age of a randomly selected Chief will be in the following range. a. Between 54 and 58 years old b. Between 56 and 65 years old c. Between 53 and 57 years old

Answer 1

Solution :

Given that ,

mean =   = 56

standard deviation = = 4

(A)P(54< x < 58) = P[(54-56) / 4< (x - ) / < (58-56) / 4)]

= P( -0.5< Z < 0.5)

= P(Z <0.5 ) - P(Z <-0.5 )

Using z table   

= 0.6915-0.3085

probability= 0.3830

(B)

P(56< x < 65) = P[(56-56) / 4< (x - ) / < (65-56) / 4)]

= P( 0< Z < 2.25)

= P(Z <2.25) - P(Z <0 )

Using z table   

= 0.9878-0.5

probability= 0.4878

(C)

P(53< x < 57) = P[(53-56) / 4< (x - ) / < (57-56) / 4)]

= P( -0.75< Z < 0.25)

= P(Z <0.25) - P(Z <-0.75 )

Using z table   

= 0.5987-0.2266

probability= 0.3721