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 of less than 84 is ___.
A)0.9332
B)0.0668
C)0.4332
D)0.8664
E)1.0000

Question

Quizplus · Accepted Answer

First we need to calculate the standard error of the mean (SEM) using the following formula:
SEM = σ/√n
where σ is the population standard deviation, n is the sample size.
SEM = 28/√49 = 4

Next, we need to standardize the sample mean using the following formula:
z = (x - μ)/SEM
where x is the sample mean, μ is the population mean, SEM is the standard error of the mean.
z = (84 - 90)/4 = -1.5

We need to find the probability of drawing a sample with a mean of less than 84, which is the same as finding the probability of z being less than -1.5. Using a standard normal distribution table or calculator, we find that the probability is approximately 0.0668. Therefore, the answer is B.

Suppose a Population Has a Mean of 90 and a Standard