Question

30% of households in a large population have a total annual income of $80,000. A simple random sample of 4 of these households is selected. What is the probability that 2 or more of the households in the survey have an annual income of $70,000? (Assume household incomes are independent)

A) 0.3456
B) 0.3483
C) 0.5000
D) 0.5248
E) 0.0837

Answer 1

The probability that 2 or more of the households in the survey have an annual income of $70,000 is 0.3483.

Step-by-step explanation:

To find the probability that 2 or more of the households in the survey have an annual income of $70,000, we can use the binomial probability formula.

The formula is:

P(X >= 2) = 1 - P(X = 0) - P(X = 1)

Where X is the number of households with an annual income of $70,000.

Let's calculate each probability:

P(X = 0) = (0.7)^4 = 0.2401

P(X = 1) = 4 * (0.3)(0.7)^3 = 0.4116

Now we can calculate the probability that 2 or more households have an annual income of $70,000:

P(X >= 2) = 1 - P(X = 0) - P(X = 1) = 1 - 0.2401 - 0.4116 = 0.3483