Getting a Number that Doesn't Make Sense to Me

Question

Information about question: the duration of a movie trailer is approximately normal, with mean 150 seconds and standard deviation 30 seconds.

One part in the questions is not making sense to me and I'm pretty sure I'm doing it okay: Any movie trailer that lasts beyond 4 minutes and 30 seconds is considered too long. What proportion of movie trailers is too long?

Obviously, I converted to seconds and wrote: $P(X>270)$

After I standardized it: $1-P(Z<4)$

But I don't find a $4$ on my table. Am I doing something wrong?

Answer 1

I don't think you are doing anything wrong. Most books show probabilities for $z \le 2.5$ or 3. A quick Google search returned a few that go up to 3.5, none of them to 4. The reason very likely is that they only show 4 or 5 decimal places, and in that case $P(z<4) = 1.00000$. I checked on Excel, it returns 0.999968329. Yes, four standard deviations is really that far out!

Answer 2

$4$ standard deviations away from the mean is so unlikely under a normal distribution that they aren't on most z-tables. You might as well simply say that the proportion of movie trailers that are too long is $0.0000$.