Question

Suppose that 30% of a large community are smokers and consider a random sample of 15 people from the community. a. Carefully explain why a binomial model may be used here. b. Find the probability (to 4 decimal places) that at least two people smoke. c. Find the mean and standard deviation of the number of non-smokers in the sample. Embed Kaltura Media.

Answer 1

a)
Here binomial model is appropriate to use with n = 15 and p = 0.3 because
A person is independently a smoker
There are only two possible outcomes
There are finite trials

b)
Here, n = 15, p = 0.3, (1 - p) = 0.7 and x = 1
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

P(X <= 1) = (15C0 * 0.3^0 * 0.7^15) + (15C1 * 0.3^1 * 0.7^14)
P(X <= 1) = 0.0047 + 0.0305
P(X <= 1) = 0.0352

required probability = 1 - 0.0352 = 0.9648

c)
mean = np = 15*0.3 = 4.5
sd = sqrt(15*0.3*0.7) = 1.7748