A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5.What is the probability of selecting a sample mean of 13 or larger from this population?
A)equal to the probability of selecting a score above the mean
B)about one standard deviation below the mean
C)less than .03
D)greater than .31

Question

Quizplus · Accepted Answer

We can use the formula for the standard error of the mean, which is σ/√n, where σ is the population standard deviation and n is the sample size. Plugging in the values, we get a standard error of the mean of 0.5. To find the probability of selecting a sample mean of 13 or larger, we need to standardize this value by subtracting the population mean from 13 and dividing by the standard error of the mean: (13-12)/0.5 = 2. The probability of selecting a sample mean of 13 or larger is then equal to the probability of selecting a value 2 standard deviations or more above the mean in a normal distribution. This probability is less than 0.03 (found using a z-table or calculator). Therefore, the answer is C.

A Researcher Selects a Sample of 49 Participants from a Population