Question

10. According to an article, 24.6% of Internet stocks that entered the market in 1999 ended up trading below their initial offering prices. If you were an investor who purchased four Internet stocks at their initial offering prices, what was the probability that at least three of them would end up trading at or above their initial offering price? (Round your answer to four decimal places.)

P(X ≥ 3) =

11. In a large on-the-job training program, half of the participants are female and half are male. In a random sample of four participants, what is the probability that an investigator will draw at least one male?† (Round your answer to four decimal places.)

P(X ≥ 1) =

12. In a large on-the-job training program, half of the participants are female and half are male. In a random sample of five participants, what is the probability that an investigator will draw at least two males?† (Round your answer to four decimal places.)

P(X ≥ 2) =

Answer 1

10)

Here, n = 4, p = 0.246, (1 - p) = 0.754 and x = 3
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 3).
P(X >= 3) = (4C3 * 0.246^3 * 0.754^1) + (4C4 * 0.246^4 * 0.754^0)
P(X >= 3) = 0.0449 + 0.0037
P(X >= 3) = 0.0486

11)

Here, n = 4, p = 0.5, (1 - p) = 0.5 and x = 1
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 1).
P(X >= 1) = (4C1 * 0.5^1 * 0.5^3) + (4C2 * 0.5^2 * 0.5^2) + (4C3 * 0.5^3 * 0.5^1) + (4C4 * 0.5^4 * 0.5^0)
P(X >= 1) = 0.25 + 0.375 + 0.25 + 0.0625
P(X >= 1) = 0.9375

12)

Here, n = 4, p = 0.5, (1 - p) = 0.5 and x = 2
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 2).
P(X >= 2) = (4C2 * 0.5^2 * 0.5^2) + (4C3 * 0.5^3 * 0.5^1) + (4C4 * 0.5^4 * 0.5^0)
P(X >= 2) = 0.375 + 0.25 + 0.0625
P(X >= 2) = 0.6875