4. A human gene carries a certain disease from the mother to the child with a probability rate of 20%. That is, there is a 20% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has four children. Assume that the infections of the four children are independent of one another. Find the probability that at least two of the children does not get the disease from their mother. (a) 0.9984 (b) 0.9728 (c) 0.9744 (d) 0.0256 5. In a fair die tossing experiment, the mean and variance of random variable X = number of dot(s) observed in a single toss are: (a) 3.50 and 2.92 (b) 3.50 and 11.67 (c) 3.50 and 15.17 (d) 3.50 and 18.00 6. It a recent study of college students indicated that 30% of all college students had at least one tattoo. A small private college decided to randomly and independently sample 15 of their students and ask if they have a tattoo. Find the standard deviation for this random variable. (a) 4.5 (b) 3.15 (c) 1.77 (d) 10.5 7. At an investment firm, 62% of the buy recommendations on stocks are made by advisor A. The remaining 38% of the buy recommendations are made by advisor B. Of the recommendations made by advisor A, 55% are good buys. Of the recommendations made by advisor B, 70% are good buys. What is the probability that a randomly selected stock recommendation, which is a good buy, was recommended by advisor A? (a) 0.3410 (b) 0.5500 (c) 0.6200 (d) 0.5618 8. In a pizza takeout restaurant, the following probability distribution was obtained. The random variable X represents the number of toppings for a large pizza. Find the mean for the random variable X. X 0 1 2 3 4 P(X) 0.3 0.4 0.2 0.06 0.04 (a) 1.14 (b)1.54 (c) 1.30 (d)1.30