Suppose 30% of a population possess a given characteristic.If a random sample of size 1200 is drawn from the population, then the probability that less than 348 possess that characteristic is ___.
A)0.2236
B)0.2764
C)0.2900
D)0.7764
E)0.3336

Question

Quizplus · Accepted Answer

The sample proportion follows a normal distribution with mean 0.3 and standard deviation sqrt(0.3*0.7/1200). Converting 348 to a proportion (348/1200 = 0.29) and finding the z-score, we get z = (0.29 - 0.3) / sqrt(0.3*0.7/1200) ≈ -0.385. Using the standard normal distribution table, the probability corresponding to z = -0.385 is approximately 0.2236.

Suppose 30% of a Population Possess a Given Characteristic