Question

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.

Answer 1

a) 0.3277

b) 0.0128

Explanation:

We are given the following information in the question:

N(2750, 560).

Mean, μ = 2750

Standard Deviation, σ = 560

We are given that the distribution of distribution of birth weights is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

a) P (less than 2500 grams)

P(x < 2500)

`P( x < 2500) = P( z < \displaystyle(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(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\%`