# Standardized Normal Distribution.

Calcium levels in people are normally distributed with a mean of $9.5$ mg/dL and a standard deviation of $0.4$ mg/dL. Individuals with calcium levels in the bottom $15\%$ of the population are considered to have low calcium levels. Find the calcium level that is the borderline between low calcium levels and those not considered low. Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.

I tried to calculate it $Z=X-9.5/0.4$.

How do I get the Z?

• You need $(X-9.5)/0.4,$ not $X-9.5/0.4. \qquad$ – Michael Hardy Apr 7 '18 at 1:36

You need to find $x$ such that $P(X\le x)=0.15$. Since $0.15<0.5$, we will take the upper $0.15$ instead. You have that \begin{align}0.15=P(X\le x)=P\left(Z\le \frac{x-9.5}{0.4}\right)=\Phi\left(\frac{x-9.5}{0.4}\right)=1-\Phi\left(\frac{9.5-x}{0.4}\right)\end{align} Hence, from the standardized normal distribution table, you find that $$\Phi(1.03643)=0.85$$ So, you need to solve $1.03643=\frac{9.5-x}{0.4}$.