Suppose a population has a mean of 400 and a standard deviation of 24.If a random sample of size 144 is drawn from the population,the probability of drawing a sample with a mean less than 402 is _______.
A) 0.3413
B) 0.6826
C) 0.8413
D) 0.1587
E) 0.9875

Question

Quizplus · Accepted Answer

The sampling distribution of the sample means will have a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size:

standard deviation = 24 / sqrt(144) = 2

To find the probability of drawing a sample with a mean less than 402, we need to standardize the sample mean using the formula:

z = (sample mean - population mean) / standard deviation

z = (402 - 400) / 2 = 1

Using a standard normal distribution table or calculator, we can find that the probability of drawing a sample with a z-score less than 1 is approximately 0.8413. Therefore, the answer is choice C.

Suppose a Population Has a Mean of 400 and a Standard