p sample, june 27

See here.

525: people watching television

I was prepared for this one to be tricker than it was. The data gave all eight of the intersections $\text{sports}\cap\text{movies}\cap\text{news}$ and their complements, which I spent a while duplicating and sanity-checking. Then it was just a matter of figuring out which four of the eight partitions went into the result.

526: tornado damage

A company insures homes in 50 different territories. The company models annual tornado losses within each territory by an exponential distribution with mean 100,000. Because of the local nature of most tornadoes, losses in one territory are independent of losses in other territories. Calculate the approximate probability that total annual tornado losses over all 50 territories exceed 5.5 million.

I guess the way that I'm using "exponentially distributed" isn't right yet: I tried to do a Poisson integral, but I think I found the probability that a single area exceeds fifty-five times the expected loss.

When your result comes out as $e^{-55}$, you've definitely done something wrong.

I punted pretty quickly (four minutes) and came back later. The second try I realized it was something to do with the counting statistics, and guessed it was a two-sigma variation. But I didn't put the counting statistics in the right place. The standard deviation should have been $\sigma = \sqrt{50}\times\$0.1M \approx \$0.7M$, so it was a one-sigma deviation (or a little less, even) instead of two. One sigma would be 30%, but I only want the high side. So I still would have guessed the lowest answer. I think I needed to look at some $z$-score table.

98: safe driving bonus

Quick and easy — except that I forgot that the question made it easy to compute a monthly expense, while the answers were about an annual expense. At least there wasn't a distractor that was one-twelfth of the correct answer.

99: set intersections

Fine. Practice will make these quicker.