Probability math

Question

Every mushroom is edible with the probabiloity 0.95, independent of other picked mushrooms.

What would be the the probability that 300 are edible amongst 320 picked? And how many mushrooms would have had to be picked so that the probability that at least 300 would be edible would be at least 0.99?

Answer 1

P(m is e) = .95

320 m selected

P(300 m are e) = ?

300 out of 320 = 93.75%

expected e out of 320 m would be .95(320 = 304

300 is slightly less than expected

P(m is not e) = .05=q, .95=p, mean=np, standard deviation = sqr(npq)= about 3.9 = about 4

one standard deviation below the mean is greater than (1-.68)/2 = .32/2 = .16

P(at least 300 out of 320) = about .84% using the empirical rule and binomial as an approximation to the normal distribution

for more precise calculation, use z tables or a z calculator

with z = (300-304)/sqr(320(.95)(.05))= about -4/3.9