A sample of 51 observations will be taken from an infinite population. The population proportion equals 0.85. The probability that the sample proportion will be between 0.9115 and 0.946 is
A)0.8633
B)0.6900
C)0.0819
D)0.0345

Question

Quizplus · Accepted Answer

The sample size is greater than 30, which means we can use the normal distribution to approximate the sampling distribution of the sample proportion. The mean of the sampling distribution is equal to the population proportion, which is 0.85. The standard deviation of the sampling distribution is equal to the square root of [(population proportion x (1 - population proportion)) / sample size], which is sqrt[(0.85 x 0.15) / 51] = 0.0617.

To find the probability that the sample proportion will be between 0.9115 and 0.946, we need to standardize these values using the sampling distribution.

Z1 = (0.9115 - 0.85) / 0.0617 = 1.00
Z2 = (0.946 - 0.85) / 0.0617 = 1.55

Using a standard normal distribution table or calculator, we can find the probability that Z is between 1.00 and 1.55, which is 0.0819. Therefore, the answer is C.

A Sample of 51 Observations Will Be Taken from an Infinite