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

Question

Quizplus · Accepted Answer

The expected number of people with green eyes in the sample is 0.3 * 1200 = 360. The standard deviation is sqrt(1200 * 0.3 * 0.7) ≈ 15.87. Using the normal approximation, the z-score for 348 is (348 - 360) / 15.87 ≈ -0.756. The probability of a z-score less than -0.756 is approximately 0.2236.