Question

The length of an instant message conversation is normally distributed with a mean of 5 minutes and a standard deviation of .7 minutes. What is the probability that a conversation lasts longer than 6 minutes?

Answer 1

The correct answer is:

0.0764

Explanation:

We will use a z-score to answer this.  The formula for a z-score is

$z=\frac{X-\mu}{\sigma}$, where μ is the mean and σ is the standard deviation.  Using our information in this problem, we have

$z=\frac{6-5}{0.7}=\frac{1}{0.7}=1.43$

Using a z-table, we look up the z-score 1.43.  The area under the curve to the left of, or less than, this value is 0.9236.  This means the probability that the time is greater than this is 1-0.9236 = 0.0764.

Answer 2

The z-score for 6 minutes is:
$z=\frac{X-\mu}{\sigma}=\frac{6-5}{0.7}=1.429$
Reference to a standard normal distribution table gives the result:
P(length > 6) = 0.077