The z-score for 5 minutes is found from:
[tex]z=\frac{X-\mu}{\sigma}
[/tex]
[tex]z=\frac{5-4}{0.6}=1.667[/tex]
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.
