Suppose a population has a mean of 90 and a standard deviation of 28.If a random sample of size 49 is drawn from the population, the probability of drawing a sample with a mean between 80 and 100 is ___.
A)0.9876
B)0.0124
C)0.4938
D)0.0062
E)1.0000

Question

Quizplus · Accepted Answer

We can use the central limit theorem to approximate the distribution of sample means as a normal distribution, where the mean of the sample means is equal to the mean of the population (90) and the standard deviation of the sample means (also known as the standard error) is equal to the standard deviation of the population (28) divided by the square root of the sample size (√49 or 7).

z-score for a sample mean of 80:

z = (80-90) / (28/7) = -2.5

z-score for a sample mean of 100:

z = (100-90) / (28/7) = 2.5

Using a standard normal distribution table or calculator, the probability of getting a sample mean between -2.5 and 2.5 is approximately 0.9876. Therefore, the answer is A.

Suppose a Population Has a Mean of 90 and a Standard