Question

For a binomial process, the probability of success is 40 percent and the number of trials is 5.

a. Find P(X > 4) (round to four decimal places).
b. Find P(X ≤ 1) (round to four decimal places).
c. Find the standard deviation (round to three decimal places).

Answer 1

a. To find P(X > 4), use the binomial distribution formula. b. To find P(X ≤ 1), use the binomial distribution formula. c. The standard deviation can be calculated using σ = √(npq).

Step-by-step explanation:

a. To find P(X > 4), we need to calculate the probability of getting 5 successes, since that is the maximum value we are interested in. Given that the probability of success is 40%, we can use the binomial distribution formula. P(X = k) = (nCk) * (p^k) * (q^(n-k)), where n is the number of trials, k is the number of successes, p is the probability of success, and q is (1 - p). Therefore, P(X > 4) = P(X = 5) = (5C5) * (0.4^5) * (0.6^(5-5)).

b. To find P(X ≤ 1), we need to calculate the probability of getting 0 or 1 success. Using the binomial distribution formula, P(X ≤ 1) = P(X = 0) + P(X = 1) = (5C0) * (0.4^0) * (0.6^(5-0)) + (5C1) * (0.4^1) * (0.6^(5-1)).

c. The standard deviation can be calculated using the formula σ = √(npq), where n is the number of trials, p is the probability of success, and q is (1 - p). Therefore, the standard deviation for this binomial process is √(5 * 0.4 * 0.6).