Question

Suppose the weights of newborn babies is normally distributed with a mean of 7 lbs and a standard deviation of 1.5 pounds. How much would a baby have to weigh to be in the top 10% of birthweights?

a.

8.5

b.

5.08

c.

8.35

d.

7.15

e.

8.92

Answer 1

Normal distribution: P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = 7 lbs

Standard deviation = 1.5 lbs

The the weight to be in top 10% be T

P(X > T) = 0.10

P(X < T) = 1 - 0.10 = 0.90

P(Z < (T - 7)/1.5) = 0.90

Take the value of Z corresponding to 0.90 from standard normal distribution table.

(T - 7)/1.5 = 1.28

T = 8.92 lbs

Ans: e. 8.92