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=(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=(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 %