Question

The distribution of total body protein in healthy adult men is approximately Normal with mean 12.3 kg and standard deviation 0.1 kg. The first quartile of the distribution of cholesterol production is

Answer 1

You want to find the amount of protein \(X=k\) that gives \(P(X<k)=0.25\). To do this, transform to the standard normal distribution:
\[\begin{align*}
P(X<k)&=P\left(\frac{X-12.3}{0.1}<\frac{k-12.3}{0.1}\right)\\\\
0.25&=P\left(Z<\frac{k-12.3}{0.1}\right)
\end{align*}\]
Given that \(P(Z<-0.675)\approx0.25\), you can set these cut-off values equal to each other:
\[\frac{k-12.3}{0.1}=-0.675~~\iff~~k=12.23\]
This means anyone with 12.23 kg of protein falls in the first quartile.

Answer 2

*with 12.23 kg or less*