Question

6) The length of a phone conversation is normally distributed with a mean of 8 minutes and a standard deviation of 0.6 minutes. What is the probability that a conversation lasts less than 9 minutes?

Answer 1

We are given a normal distribution with a mean of 8 and a standard deviation of 0.6. Since the probability is normally distributed we need first to find the z-score of the distribution, to do that we use the following formula:

$z=\frac{X-\mu}{\sigma}$

We have the following values:

$\begin{gathered} X=9 \\ \mu=8 \\ \sigma=0.6 \end{gathered}$

Replacing the values we get:

$z=\frac{9-8}{0.6}=1.67$

Now we use a normal distribution table to determine the probability for this z-score. That probability is:

$P=0.9522\approx95.22percent$

Therefore, the probability is 95.22 %