Chapter 5, Problem 1P

Because serum cholesterol is related to age and sex, some investigators prefer to express it in terms of z-scores. If X = raw serum cholesterol, then $Z=\frac{X-\mu }{\sigma }$, where μ is the mean and σ is the standard deviation of serum cholesterol for a given age–gender group. Suppose Z is regarded as a standard normal random variable.

What is Pr(Z < 0.5)?

To determine

Find probability $P\left(Z<0.5\right)$.

Answer to Problem 1P

Probability, $P\left(Z<0.5\right)$, is 0.6915.

Explanation of Solution

Step-by step procedure to obtain the probability value using software is given below:

• Open an EXCEL sheet.
• In cell A1, enter “=NORM.S.DIST(0.5,1)”.
• Click Enter.

The output obtained is shown below:

Thus, the probability, $P\left(Z<0.5\right)$,is 0.6915.