
I have another question
A financial analyst claims to be able to spot companies that are likely candidates for bankruptcy. The analyst is presented with information on the past records of 15 companies and is told that 5 of these have failed. He selects as candidates for failure 5 companies from the group of 15. In fact, 3 of the 5 companies selected by the analyst where among those that failed. Evaluate the fiancial analyst performance on this test of his ability to detect failed companies.
I am giving in..

1) Very bad test. The results were biased when the analyst was told that there were 5 failures. Without this informatio, he may have chose 3 or 7 or whatever.
2) Throwing darts, one can expect 1.67 (If I counted correctly) correct responses, with standard deviation 1.89. This puts him only 0.71 SD above the mean with a very rough normal approximation. I'm not very impressed.
If he had gotten 4 correct, I would be more impressed, but even that forces me to overlook testing error #1. Very bad. Make him prove it before you offer him the big bucks.

Thank you TKHunny. But I , I just think this is more than I was expected to do, because the result on my book says "To evaluate the effectiveness of the analyst ability, find the probability that x is greater than or equal to 3 at random P(x>=3) = 0. 16683 "
What does this mean? Thank you again.

It means you can hire monkeys and get more than 3 correct 1/6 of the time. You also would have to pay them a lot less.