Question

Low birth weights are considered to be less than 2500 g for newborns. Birth weights are normally distributed with a mean of 3150 g and a standard deviation of 700 g.

a) If a birth weight is randomly selected what is the probability that it is a low birth weight?

b) Find the weights considered to be significantly low using the criterion of a probability of 0.02 or less. That is, find the weight ranked as the lowest 2%.

c) Find the weight ranked as the highest 2%

d) Find the probability of a birth weight between 2600 g and 3500 g.

Answer 1

a)

Here, μ = 3150, σ = 700 and x = 2500. We need to compute P(X <= 2500). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (2500 - 3150)/700 = -0.93

Therefore,
P(X <= 2500) = P(z <= (2500 - 3150)/700)
= P(z <= -0.93)
= 0.1762

b)

z value at 2% = -2.05

z =(x - mean)/sigma

-2.05 = (x - 3150)/700

x = 700 * -2.05+3150
x = 1715.00

c)

z value at 2% = 2.05

z =(x - mean)/sigma

2.05 = (x - 3150)/700

x = 700 * 2.05+3150
x = 4585

d)

Here, μ = 3150, σ = 700, x1 = 2600 and x2 = 3500. We need to compute P(2600<= X <= 3500). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (2600 - 3150)/700 = -0.79
z2 = (3500 - 3150)/700 = 0.5

Therefore, we get
P(2600 <= X <= 3500) = P((3500 - 3150)/700) <= z <= (3500 - 3150)/700)
= P(-0.79 <= z <= 0.5) = P(z <= 0.5) - P(z <= -0.79)
= 0.6915 - 0.2148
= 0.4767