Question

The length of a text message is conversation is normally distributed with a mean of 2 min and a standard deviation of 0.5 min.

What is the probability that a conversation last longer than 3 min ?

Answer 1

`\mathbb P(X>3)=\mathbb P\left((X-2)/(0.5)>(3-2)/(0.5)\right)=\mathbb P(Z>2)`

About 95% of a normal distribution lies within two standard deviations of the mean, so 5% lies without, and since the distribution is symmetric, 2.5% lies to either side. This means


`\mathbb P(X>3)=\mathbb P(Z>2)\approx0.025`