Suppose 30% of the population has green eyes. If a random sample of size 1200 is drawn, then the probability that less than 348 U.S. citizens have green eyes is ___.
A) 0.2236
B) 0.2764
C) 0.2900
D) 0.7764
E) 0.3336

Question

Quizplus · Accepted Answer

The probability of a U.S. citizen having green eyes is 0.3. The probability of less than 348 U.S. citizens having green eyes is the probability of 347 or fewer U.S. citizens having green eyes. This is the sum of the probabilities of 0, 1, 2, ..., 347 U.S. citizens having green eyes. This sum can be calculated using the binomial distribution. The probability of x U.S. citizens having green eyes is given by the formula:```P(x) = (1200 choose x) * (0.3)^x * (0.7)^(1200-x)```where (1200 choose x) is the binomial coefficient, which represents the number of ways to choose x items from a set of 1200 items.The probability of less than 348 U.S. citizens having green eyes is:```P(x < 348) = P(x = 0) + P(x = 1) + ... + P(x = 347)```This sum can be calculated using a computer program. The result is 0.2236.

Suppose 30% of the Population Has Green Eyes