Question

Suppose birth weights of human babies are normally distributed with a mean of 120 ounces and a stdev of 16 ounces (1lb = 16 ounces).

1. What is the probability that a baby is at least 9 lbs 11 ounces? 2. What is the probability that a baby weighs less than 10 lbs (160 ounces)? 3. What weight is the 90th percentile?

Answer 1

Mean = u = 120 ounces

Standard deviation = s = 16 ounces

1. X = 9 lbs 11 ounces = (16*9)+11 = 155 ounces

P( X > 155 ) = ?

Z = ( X - u )/s

Z(155) = (155 - 120)/16 = 2.1875

P( X > 155 ) = P( Z > 2.1875 ) = 0.0144

2. X = 160 ounces

P( X < 160 ) = ?

Z = ( X - u )/s

Z(160) = (160 - 120)/16 =

P( X < 160 ) = P( Z < 2.5) = 0.9938

3. Z score at 90th Percentile = 1.282

u = 120 , s= 16

Z = (X - u)/s

1.282 = ( X - 120)/16

X = 120 + 16*1.282 = 140.51