Question

The length of a phone conversation is normally distributed with a mean of 4 minutes and a standard deviation of 0.6 minutes. What is the probability that a conversation lasts longer than 5 minutes

Answer 1

The z-score for 5 minutes is found from:
$z=\frac{X-\mu}{\sigma}$
$z=\frac{5-4}{0.6}=1.667$
Reference to a normal distribution table shows that the cumulative probability for a z-score of 1.667 is around 0.9522.
Therefore the probability that a conversation lasts for longer than 5 minutes is:
1 - 0.9522 = 0.048 to 3 d.p.

Answer 2

The answer is A 0.54746