Moderate# Central Limit Theorem and Determining Probabilities

STATS-ABCLXD

Suppose 2500 individuals are to be selected at random and the amount of time (in minutes) their web browser is active on a given day is recorded.

Let $\bar{X}$ denote the average time these 2500 individuals spend on the web. Suppose it is also known that the mean of the time spent in a day on web browsing by all internet-connected individuals is 250 minutes with a standard deviation of 150 minutes.

Find $P(\bar{X} > 256)$, considering the following facts (where $Z$ is a standard normal random variable):

- $P(Z< 2.5)= .994$
- $P(Z< 2)=.977$
- $P(Z< 1)= .841$
- $P(Z< -1.5)= .067$