Question

[Normal] Heights for American women are normally distributed with parameters μ = 65 inches and σ = 2.5 inches.
a. What is the probability that a randomly selected woman is shorter than 63 inches?
b. What height value marks the bottom 8% of the distribution?

please show all work used to solve this problem

Answer 1

Solution :

Given that ,

mean =   = 65

standard deviation = = 2.5

P(X<63 ) = P[(X- ) / < (63-65) /2.5 ]

= P(z <-0.8 )

Using z table

= 0.2119

probability=-0.2119

(B)

Using standard normal table,

P(Z < z) = 8%

= P(Z < z) = 0.08  

= P(Z <-1.41 ) = 0.08

z =-1.41 Using standard normal z table,

Using z-score formula  

x= z * +

x= -1.41*2.5+65

x= 61.475

x=62