Q:

# How much difference do a couple of weeks make for birth weight? Late-preterm babies are born with 34 to 36 completed weeks of gestation. The distribution of birth weights (in grams) for late-preterm babies is approximately N(2750, 560).1. What is the probability that a randomly chosen late-preterm baby would have a low birth weight (less than 2500 grams)? Round your answer to 4 decimal places.2. What is the probability that a randomly chosen late-preterm baby would have a very low birth weight (less than 1500 grams)? Round your answer to 4 decimal places.

Accepted Solution

A:
Answer:a) 0.3277b) 0.0128Step-by-step explanation:We are given the following information in the question:N(2750, 560).Mean, μ = 2750Standard Deviation, σ = 560We are given that the distribution of distribution of birth weights is a bell shaped distribution that is a normal distribution.Formula:$$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$$a) P (less than 2500 grams)P(x < 2500)$$P( x < 2500) = P( z < \displaystyle\frac{2500 - 2750}{560}) = P(z < -0.4464)$$Calculation the value from standard normal z table, we have,  $$P(x < 2500) = P(z < -0.4464) = 0.3277 = 32.77\%$$b) P ((less than 1500 grams)P(x < 1500)$$P( x < 1500) = P( z < \displaystyle\frac{1500 - 2750}{560}) = P(z < -2.2321)$$Calculation the value from standard normal z table, we have,  $$P(x < 1500) = P(z < -2.2321) = 0.0128 = 1.28\%$$