- #1
toothpaste666
- 516
- 20
Homework Statement
How many times do we have to flip a balanced coin to be able to assert with a probability of at most .01 that the difference between the proportion of tails and .50 will be at least .04?
Homework Equations
P( |X-μ| ≥ kσ ) ≤ 1/k^2
The Attempt at a Solution
I am very confused about how to use this theorem. So far I have only managed to figure out bits and pieces.
I know that
P ≤ .01 = 1/k^2 so
k^2 = 1/.01 = 100
k = 10
also μ = np and since the coin is balanced, p = 1/2 so
μ = n/2
also σ^2 = np(1-p) = n/2(1/2) = n/4
so σ = sqrt(n)/2
plugging this all into the inequality I get
P( |X-n/2| ≥ (10)(sqrt(n)/2) ) ≤ .01
P( |X-n/2| ≥ (5)sqrt(n) ) ≤ .01
But I am still confused about what this means or how I can solve for n (which is what I think I need to be solving for.) please help :(