The number of kilometers traveled by usual users of an airline is a random variable $X$ with an average and standard deviation of 25,000 and 12,000 kilometers, respectively. If 30 of these people are randomly selected, calculate the probability that for the current year the average of kilometers traveled will exceed 25,000.
I understand that I have to calculate $P(\bar X \gt 25 000)$ but I do not have a track on how to do it. Can someone help me?
This problem is easier than it at first appears.
The Central Limit theorem suggests that if we average the data of enough data the expectation for the average will behave like a normally distributed random variable.
If the distribution is normal, it is symmetric about the mean.
$P(X > \mu) = 0.5$