Question

Let x represent a binomial random variable with n = 170 and p = 0.6. Find the following probabilities. (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

Answer 1

To find the probabilities for a binomial random variable with n = 170 and p = 0.6, we can use the binomial distribution formula and calculate the probabilities as follows: P(x = 100), P(x < 90), and P(x ≥ 110).

Step-by-step explanation:

To find the probabilities for a binomial random variable, we can use the binomial distribution formula. Given that x represents a binomial random variable with n = 170 and p = 0.6, we can calculate the following probabilities:

a. P(x = 100) = nCx * p^x * (1-p)^(n-x)

b. P(x < 90) = P(x ≤ 89) = P(x = 0) + P(x = 1) + ... + P(x = 89)

c. P(x ≥ 110) = 1 - P(x < 110) = 1 - P(x ≤ 109)