Question

birth weights in norway are normally distributed with a mean of 3570 g and a standard deviation of 500g. if the hospital officials plan to require special treatment for the lightest 3% of newborn babies, what birth weight seperates those requiring special treatment from those who do not

Answer 1

2630 g

Explanation:

From the given information:

Given that:

mean (μ) = 3750 g

Standard deviation (σ) = 500

Suppose the hospital officials demand special treatment with a percentage of lightest 3% (0.03) for newborn babies;

Then, the weight of birth that differentiates the babies that needed special treatment from those that do not can be computed as follows;

P(Z < z₁) = 0.03

Using the Excel Formula; =NORMSINV(0.03) = -1.88

z₁ = - 1.88

Using the test statistics z₁ formula:

`z_1 = (X-\mu)/(\sigma)`

`-1.88 = (X-3570)/(500)`

By cross multiply, we have:

-1.88 × 500 = X - 3570

-940 = X - 3570

-X = -3570 + 940

-X = -2630

X = 2630 g

Hence, 2630 g is the required weight of birth that differentiates the babies that needed special treatment from those that do not