If random variable X is distributed according to a uniform distribution between 0 and 1 (X ~ U[0,1]),and 100 random samples of sizes 35-40 were taken,the standard deviation of the sample means would be ______.
A) undetermined; there is not enough information to answer
B) between 0.0142 and 0.0151
C) between 0.0132 and 0.0141
D) between 0.0122 and 0.0131
E) between 0.0112 and 0.0121

Question

Quizplus · Accepted Answer

The standard deviation of the sample means can be calculated using the formula:
standard deviation = standard deviation of population / square root of sample size
Since X ~ U[0,1], the standard deviation of the population can be calculated as:
standard deviation of population = (1-0)/sqrt(12) = 0.2887
Using the largest sample size of 40, the standard deviation of the sample means would be:
standard deviation = 0.2887 / sqrt(40) = 0.0457
Using the smallest sample size of 35, the standard deviation of the sample means would be:
standard deviation = 0.2887 / sqrt(35) = 0.0488
Therefore, the standard deviation of the sample means would be between 0.0488 and 0.0457, which corresponds to answer choice C.

If Random Variable X Is Distributed According to a Uniform