Question

The average birth weight of domestic cats is about 3 ounces. Assume that the distribution of birth weights is normal with a standard deviation of 0.6 ounces.

a. Find the birth weight of cats at the 80th percentile

b. Find the birth weight of cats at the 20th percentile

Answer 1

Given that,

mean = = 3

standard deviation = = 0.6

Using standard normal table,

P(Z < z) = 80%

= P(Z < z) = 0.80  

= P(Z < 0.84) = 0.80

z = 0.84 Using standard normal z table,

Using z-score formula  

x= z * +

x= 0.84 *0.6+3

x= 3.504

(B)

Using standard normal table,

P(Z < z) = 20%

= P(Z < z) = 0.20  

= P(Z < -0.84) = 0.20

z = - 0.84 Using standard normal z table,

Using z-score formula  

x= z * +

x= - 0.84 *0.6+3

x= 2.496