Baby weights: According to a recent National Health Statistics Reports, the weight of male babies less than 2 months old in the United States...

Question

Baby weights: According to a recent National Health Statistics Reports, the weight of male babies less than 2 months old in the United States is normally distributed with mean 11.5 pounds and standard deviation 2.7 pounds.

c.	What proportion of babies weigh between 10 and 14 pounds?
d.	Is it unusual for a baby to weigh more than 17 pounds?

Answer 1

Knowns:

1. Mean (µ=11.5)
2. Std, Dev (σ=2.7)

c.) P(10 ≤ x ≤14)

1. Break into two pieces:
2. P(10 > x ) -> Standardize
3. P(10-11.5)/2.7 = z > (-1.5)/2.7= -0.56
4. Look at z-table (http://www.z-table.com/): P( z> -0.56) = 1-0.2877=0.7123
5. P(x < 14) -> Standardize
6. P(11.5-14)/2.7 = (-2.5)/2.7 = -0.93
7. Look at z-table (http://www.z-table.com/): P(z < -0.93) = 0.1762
8. Remember that a normal distribution is symmetrical. Thus:
9. 0.7123 - 0.1762 = 0.536
10. Therefore the probability of a male baby being between 10 and 14 pounds is 53.6%.

d.) You have to define "unusual" first. p < 0.05 is a standard metric so we will use that.

1. P(x>17) = (17-11.5)/2.7 = (6)/2.7 = 2.22
2. Look at the table (http://www.z-table.com/) which gives the probability a baby weighs less than 17 lbs which is 0.9868. Thus, the probability that P(z>2.22) = 1 - 0.9868= 0.0132
3. Since 0.0132 is less than 0.05, it would be unusual at the 5% significance level that a male baby would weigh at least 17 lbs or more. Since 0.0132 < 0.05.