1. A random variable X has a binomial distribution with mean 6 and variance 3.6. Find P(X = 4).
2. A certain type of mint has a label weight of 20.4 grams. Suppose that the probability is 0.90 that a mint weighs more than 20.7 grams. Let X equal the number of mints that weigh more than 20.7 grams in a sample of eight mints selected at random.
a) How is X distributed if we assume independence?
(i) P(X = 8)
(ii) P(X ≤ 6)
(iii) P(X ≥ 6)
3. Suppose that the percentage of American drivers who are multitaskers (e.g., talk on cell phones, eat a snack, or text message at the same time they are driving) is approximately 80%. In a random sample of n = 20 drivers, let X equal the number of multitaskers.
a) How is X distributed?
b) Give the values of the mean, variance, and standard deviation of X.
(i) P(X = 15)
(ii) P(X > 15)
(iii) P(X ≤ 15)
The solution contains the determination of p.m.f., mean and variance of a binomial distribution for several example problems.