Question

Birth weight, in grams, of newborn babies are normally distributed with a mean of 3290 grams and a standard deviation of 520 grams. Find the percentage of newborns that weigh between 3000 and 4000 grams. Consider again the birth weights of newborn babies, where the mean weight is 3290 grams and the standard deviation is 520 grams. Find the weight, in grams, that would separate the smallest 4% of weights of newborns from the rest.

Answer 1

Question 1:

Here, we are given the distribution as:

The required probability here is:

Converting this to a standard normal variable, we get:

Getting it from the standard normal tables, we get:

Therefore 62.54% is the required percentage here.

Question 2:

Here, we need to find K such that:

P(X < K ) = 0.04

From standard normal tables, we have:

P(Z < -1.751 ) = 0.04

Therefore K = 3290 -1.751*520 = 2379.48

Therefore 2379.48 gms is the required weight here.