I need help with this question for statistics:?

Question

A company claims a medication is 92% effective in relieving pain. If 10 ppl who suffer from pain are randomly selected and given the med, and assuming the claim is correct, find the probability that:
a. at least 8 will be relieved of pain
b. exactly 2 of them will not be relieved of their pain

Answer 1

X = no of people who are relieved
X ~ B(10, 0.92)

P(X = x) = nCx * p^x * q^(n-x)

P(X = 8,9,10) = 0.8742
P(X = 8) = 0.1478

Answer 2

This question requires use of the binomial distribution function. This is in any standard stats book, or at http://en.wikipedia.org/wiki/Binomial_distribution (Note here n=10, p=0.92 and k = 1...10)

Using that you can calculate the probability of there being 1, 2, 3 ....10 people relieved of pain.

To answer a it is the sum of the probabilities for 8, 9 and 10 being relieved of pain using binomial equation.

To answer b - remember that the probability of not being effective is 1-probability of being effective. Then use the binomial equation to get prob of exactly 2.

Answer 3

a) P(at least 8 relieved of pain) = P(8 relieved) + P(9 relieved) + P(10 relieved)
= 10C8 (0.92)^8 (0.08)^2 + 10C9 (0.92)^9 (0.08)^1 + (0.92)^10
where I am using the notation nCr for n choose r, i.e. n! / (r! (n-r)!); 10C8 = 45, 10C9 = 10.
= 0.14781 + 0.37773 + 0.43439
= 0.9599
So there is a 96.0% probability that at least 8 will be relieved of pain.

b) This is just the first value from the sum in the last question (2 not relieved = 8 relieved), so there is a 14.8% probability that exactly 2 will not be relieved of their pain.