Question

The probability that a randomly selected person has O+ blood type is 38%. suppose that ten people are randomly selected; let X denote the number of these people who have type O+ blood.

Find the expected value and standard deviation of X, and describe the skewness of X.

Find the probability that exactly two of the selected people will have type O+ blood. Also find the probability that at most two of the selected people will have O+ blood.

Answer 1

X ~ Bin(n, p), where, n = 10, p = 0.38

E(X) = np = 10 * 0.38 = 3.8, Var(X) = np(1-p) = 2.356,

s.d.(X) = = 1.5349.

The skewness of X = = 0.1564, hence, the distribution is slightly right skewed.

The probability that exactly 2 of the selected people have O+ type blood = P(X = 2) = = 0.1419.

The probability that at most 2 of the selected people have O+ type blood = P(X <= 2) = = 0.2017.