Question

Heights of adult emperor penguins are known to be normally distributed with an average height of 4 feet and a standard deciation of 0.8 feet. Let X be the height of a randomly selected adult emperor penguin.

1. Find P(X > 3.8).
2. Find the 95th percentile of X.

Answer 1

Solution :

Given that ,

mean = = 4

standard deviation = = 0.8

P(x > 3.8) = 1 - P(x< 3.8)

= 1 - P[(x -) / < (3.8-4) /0.8 ]

= 1 - P(z < -0.25)

Using z table

= 1 - 0.4013

= 0.5987

probability= 0.5987

B.]

Using standard normal table,

P(Z < z) = 95%

=(Z < z) = 0.95  

= P(Z < 1.65 = 0.95  

z = 1.65   

Using z-score formula  

x = z +

x = 1.65*0.8+4

x = 5.32

x=5