Question

Note: Please explain thoroughly. Thank you.

Question Suppose that 60% of all computers sold at an electronic store are laptops and 40% are desktops. The type of computer purchased by each of the next 12 customers will be noted; assume customers are independent. Define the random variable X = number of computers among these 12 that are laptops.

a. What specific distribution does X have? With what parameters?

b. What is the mean of X?

c. What is the standard deviation of X?

d. What is the probability that at least 11 computers are laptops?

Answer 1

a) X has a binomial distribution.

n = 12

p = 0.6

b) Mean = np = 12 * 0.6 = 7.2

c) Standard deviation= sqrt(np(1 - p))

                                  = sqrt(12 * 0.6 * (1 - 0.6))

                                 = 1.6971

d) P(X > 11) = P(X = 11) + P(X = 12)

                   = 12C11 * (0.6)^11 * (0.4)^1 + 12C12 * (0.6)^12 * (0.4)^0

                   = 0.0196