Question

12#Suppose that the hemoglobin levels among healthy females are normally distributed with a mean of 14.2 g/dL. Research shows that exactly 95% of healthy females have a hemoglobin level below 15.9 g/dL. What is the standard deviation of the distribution of hemoglobin levels in healthy females? Carry your intermediate computations to at least four decimal places. Round your answer to at least two decimal places.

Answer 1

The Solution:

Given:

$\begin{gathered} \mu=14.2\text{ }g\text{ /}dL \\ P(Z=\bar{x})=95\text{ \%}=0.95 \\ \bar{x}=15.9\text{ g/dL} \\ \sigma=? \end{gathered}$

Required:

Find the standard deviation of the distribution of hemoglobin levels in healthy females.

From the Z-score tables, 95% of healthy females is:

$P(Z=x)=1.65$

Formula:

$P(Z=\bar{x})=\frac{\bar{x}-\mu}{\sigma}$

Substitute:

$1.65=\frac{15.9-14.2}{\sigma}$$\sigma=\frac{1.7}{1.65}=1.03$

Answer:

1.03