Question

In a certain population of Drosophilae (i.e., flies), 70 percent of the flies are black and 30 percent are grey. Suppose we intend to sample 8 flies from the population.

A. What is the probability that we will observe at most 3 black flies?

B. Suppose we intend to sample 100 flies from the population. What is the mean of number of grey flies?

C. Suppose we intend to sample 100 flies from the population. What is the standard deviation of the numbers of grey flies?

(Round your answers to three digits after the decimal points.)

Answer 1

a) P(black files) = 0.7

n = 8

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

              = 8C0 * 0.7⁰ * 0.3⁸ + 8C1 * 0.7¹ * 0.3⁷ + 8C2 * 0.7² * 0.3⁶ + 8C3 * 0.7³ * 0.3⁵

              = 0.058

b) p = P(grey) = 0.3

n = 100

Mean = n * p = 100 * 0.3 = 30

c) standard deviation = sqrt(n * p * (1 - p)) = sqrt(100 * 0.3 * 0.7) = 4.583