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

1 - 0.9522 = 0.048 to 3 d.p.

Explanation:

Answer 2

The z-score for 5 minutes is found from:

`z=(X-\mu)/(\sigma)`

`z=(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.