1. Consider a binomial random variable with n = 6 and p = 0.8. Let x be the number of successes in the sample. (Round your answers to three decimal places.)

(a) Find the probability that x is 3 or less.

(b) Find the probability that x is 3 or more.

(c) Find P(x < 3).

(d) Find P(x = 3).

(e) Find P(3 ≤ x ≤ 4).

2. Let x be a binomial random variable with n = 5, p = 0.2. Find the following values. (Round your answers to three decimal places.)

(a) P(x = 4)

P(x = 4) =

(b) P(x ≤ 1)

P(x ≤ 1) =

(c) P(x > 1)

P(x > 1) =

(d) μ = np

μ =

(e) σ = sq rt of npq

σ =

3. Find P(x ≤ k) for each of the following cases. (Round your answers to three decimal places.)

(a) n = 20, p = 0.05, k = 2

(b) n = 15, p = 0.7, k = 8

(c) n = 10, p = 0.9, k = 9

4. Find the mean μ and standard deviation σ for a binomial distribution with n = 100 and the following values of p. (Round your answers to two decimal places.)

(a) p = 0.01

μ =
σ =

(b) p = 0.9

μ =
σ =

(c) p = 0.2

μ =
σ =

(d) p = 0.8

μ =
σ =

(e) p = 0.5

μ =

σ = 5. According to the Humane Society of the United States, there are approximately 77.5 million owned dogs in the United States, and approximately 40% of all U.S. households own at least one dog.† Suppose that the 40% figure is correct and that 15 households are randomly selected for a pet ownership survey. (a) What is the probability that exactly seven of the households have at least one dog? (Round your answer to three decimal places.) (b) What is the probability that at most five of the households have at least one dog? (Round your answer to three decimal places.) (c) What is the probability that more than 10 households have at least one dog? (Round your answer to three decimal places.)