For the 2017 NFL regular season, tickets sold at the ticket-office for a certain game is a random variable with mean=2.4 and variance=4. Suppose that a couple of hours before the game starts, 100 fans would like to get tickets on the ticket office. If there are only 250 tickets left, what is the probability that every single one of them gets a ticket?
Im thinking something along the way of the Central Limit Theorem, but Im actually not sure... Thanks in advance.
well question is what is the probability of:
type of distribution is unknown but we could write this... $X_n \sim N(2.4, 4)$
this is your problem $P(X_1 + X_2 + ... + X_{100} >= 250) = ?$ which means
$P(X_1 + X_2 + ... + X_{100} >= 250) = P((\overline X - 2.4) / (2/10) >= ((250/100) - 2.4)/(2/10)) = ? $
where $\overline X \sim N(0, 1)$
and now you have CLE problem to solve