Question is: Experience has shown that 53% of all patients with a certain disease will recover if given the standard treatment.
a) If 90 patients with the disease are chosen at random, what is the probability that at least 40 will recover if each patient is given the standard treatment?
b) What is the smallest number of patients needed to be selected at random if there is at least 95% probability that there are at least 10 patients who will recover? For this number of patients that are selected, compute the exact probability that there are at least 10 patients who will recover.
for part a, I think its in poisson distribution so I'm assuming n = 90, p=.53 and since np = lamda; lamda = 47.7 with x = 40. This means that I need to find P(X > 40) which is equivalent to 1 - P(X<=40) getting the answer to be .852 (can't be sure if this should be solved in binomial distribution or poisson distribution)
for part b, I think the question is asking P(10>X>=x)>.95; is this correct? if so, should this be solved by using binomial dist or poisson dist?
with sincere thanks, jane