A population has a mean of 300 and a standard deviation of 18.A sample of 144 observations will be taken.The probability that the sample mean will be between 297 to 303 is
A) 0.4332.
B) 0.9544.
C) 0.9332.
D) 0.0668.

Question

Quizplus · Accepted Answer

We can use the central limit theorem to approximate the distribution of the sample mean. The mean of the sample mean distribution will be equal to the population mean (300), and the standard deviation of the sample mean distribution (also known as the standard error) will be equal to the population standard deviation divided by the square root of the sample size (18/sqrt(144) = 1.5).

Now we want to find the probability that the sample mean will be between 297 and 303. We can standardize this interval by subtracting the mean of the sample mean distribution (300) and dividing by the standard deviation of the sample mean distribution (1.5):

(z-score for 297) = (297 - 300) / 1.5 = -2
(z-score for 303) = (303 - 300) / 1.5 = 2

Using a standard normal distribution table or calculator, we can find the probability of the sample mean being between -2 and 2 to be approximately 0.9544. Therefore, the answer is B.

A Population Has a Mean of 300 and a Standard