A random sample of size 100 is taken from a population described by the proportion p = 0.60. The probability that the sample proportion is less than 0.55 is ________.
A) ≈0
B) 0.1537
C) 0.3669
D) 0.8461

Question

Quizplus · Accepted Answer

The probability that the sample proportion is less than 0.55 can be found using the normal approximation to the binomial distribution. The mean of the sampling distribution of the sample proportion is p = 0.60, and the standard deviation is sqrt[(p(1-p))/n] = sqrt[(0.6*0.4)/100] = 0.049. Using the Z-score formula, Z = (0.55 - 0.60) / 0.049 ≈ -1.02. Looking up this Z-value in a standard normal distribution table or using a calculator gives a probability of approximately 0.1537.

A Random Sample of Size 100 Is Taken from a Population