Select the correct answer.
The results of a series of surveys revealed a population with a mean of 4.73 and a standard deviation of 0.865. If each survey has a sample size of 200, which value falls within the interval where 95% of the sample means occur?
A.
4.55
B.
4.63
C.
4.88
D.
4.91
The correct answer is C. 4.88.
To find the value that falls within the interval where 95% of the sample means occur, we can use the formula for the margin of error:
Margin of Error = z * (standard deviation / √sample size)
The z-value that corresponds to a 95% confidence level is 1.96 (from the standard normal distribution).
Plugging in the values from the problem:
Margin of Error = 1.96 * (0.865 / √200) ≈ 0.1201
To find the upper limit of the interval, we add the margin of error to the mean:
Upper limit = mean + margin of error = 4.73 + 0.1201 = 4.85
Therefore, the value that falls within the interval where 95% of the sample means occur is 4.88 (option C).