Question

3. It is commonly believed that 10% of Americans are left-handed. Find the probability that in a random sample of twelve Americans –

(a) exactly three are left-handed.


(b) fewer than three are left-handed.

Answer 1

Q.3) Let X be a number of left-handed among 12 Americans and P(left-handed) = P(success) = p = 0.10

Here, X ~ Binomial (n = 12, p = 0.10)

a) We want to find, P(X = 3)

Therefore, the probabilitiy that exactly three are left-handed is 0.0852

b) We want to find, P(X < 3)

Therefore,bthe probabilitiy that fewer than three are left-handed is 0.8891