Question

Question 3 (4 points)The length of a text messaging conversation is normally distributed with a mean of 2 minutes and a standard deviation of 0.5 minutes.What is the probability that a conversation lasts longer than 3 minutes? (4 points)Оа0.043351Ob0.0637480.02275Od0.095424Submit

Answer 1

We have a normal distribution for our variable, with mean 2 and standard deviation of 0.5 minutes.

We have to calculate the probability that the variable takes a value of 3 or more.

If we calculate the z value, we get:

$z=\frac{X-\mu}{\sigma}=\frac{3-2}{0.5}=\frac{1}{0.5}=2$

Then, the probability we are looking for is:

$P(X>3)=\Phi(z>2)$

We can look for this probability in a standard normal distribution table or use an app, and its value will be 0.02275.