Question

A normally distributed dataset has a mean of 20and a standard deviation of 25. What is theprobability that a randomly selected variable fromthis dataset is positive?

Answer 1

The probability that a randomly selected variable is positive is the same as P(X>0).

The z-score for X=0 is:

$z=\frac{X-\mu}{\sigma}=\frac{0-20}{25}=\frac{-20}{25}=-\frac{4}{5}=-0.8.$

From the standard normal distribution table, P(z<-0.8) has the probability:

$P(z<-0.8)=0.21186$

It follows that:

$\begin{gathered} P(z>-0.8)=1-P(z<-0.8)=1-0.21186 \\ \Rightarrow P(z>-0.8)=0.78814\approx0.788 \end{gathered}$

Hence, the required probability is about 0.788.

The answer is 0.788.