Error Calculation Homework: Can I Kill 1 Bird with 2 Shots?

[pangru]

Homework Statement

I have to shot 100(±5) to kill 50.
how many shots I need to kill 1 bird?

Homework Equations

The Attempt at a Solution

100±5/50 = 2±0.1

this solution is so simple, I think it is not right - is it?

 

[BvU]

Mathematically speaking, the question "how many shots do I need to kill 1 bird" can be interpreted as : "after how many shots is the probability that one single bird that I am shooting at is dead" ? And that can be answered with: an infinite number of shots. Because there is a non-zero probability that you miss N shots, however big you choose N.

After which the bird will fly away.

However, things change when you ask (for example) : after how many shots can I be 95% certain the bugger is dead.

PS in your answer, if you want to be on the safe side: how does one fire 2.1 shots ?

 

[Buzz Bloom]

Hi pangru:

The "+/- 5" represents some form of "standard error" which is some multiple of the standard deviation of a distribution. From

https://en.wikipedia.org/wiki/Standard_deviation​

"the population standard deviation is equal to the square root of the variance".
The variance is proportional to the sample size. In the problem example, the sample size of 100 produced the standard deviation of 5. From that you are to estimate the standard deviation for a sample size of 2. The answer you got of 0.1 by dividing by 50 is wrong.

Hope this helps.

Regards,
Buzz