Question

A certain type of tomato seed germinates 90% of the time. A backyard farmer planted 25 seeds.

a) What is the probability that exactly 20 germinate? Carry answer to the nearest ten-thousandths.

b) What is the probability that 20 or more germinate? Carry answer to the nearest ten-thousandths.

c) What is the probability that 24 or fewer germinate? Carry answer to the nearest ten-thousandths. d) What is the expected number of seeds that germinate? Carry answer to the nearest tenths.

Answer 1

n = 25

p = 0.9

It is a binomial distribution.

P(X = x) = nCx * p^x * (1 - p)^{n - x}

a) P(X = 20) = 25C20 * (0.9)^20 * (0.1)^5 = 0.0646

b) P(X > 20) = P(X = 20) + P(X = 21) + P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25)

                     = 25C20 * (0.9)^20 * (0.1)^5 + 25C21 * (0.9)^21 * (0.1)^4 + 25C22 * (0.9)^22 * (0.1)^3 + 25C23 * (0.9)^23 * (0.1)^2 + 25C24 * (0.9)^24 * (0.1)^1 + 25C25 * (0.9)^25 * (0.1)^0

                     = 0.9666

c) P(X < 24) = 1 - P(X > 24)

                    = 1 - P(X = 25)

                    = 1 - 25C25 * (0.9)^25 * (0.1)^0

                    = 1 - 0.0718

                    = 0.9282

d) Expected value = n * p = 25 * 0.9 = 22.5