Question

Shown below is the sampling distribution of samples of size n=2 obtained from a population that consists of the elements 1, 2, 3, and 4. If a sample is randomly taken from the population, what is the probability that its sample mean is 2.5? *

Answer 1

To calculate the probability that the sample mean is 2.5, we need to examine the sampling distribution provided.

Sampling Distribution:

Sample Mean | Probability

1.5 | 1/16

2.0 | 4/16

2.5 | 6/16

3.0 | 4/16

3.5 | 1/16

The probability that the sample mean is 2.5 can be obtained by summing up the probabilities associated with that value:

Probability(sample mean = 2.5) = 6/16 = 3/8 = 0.375

Therefore, the probability that a randomly taken sample from the population will have a sample mean of 2.5 is 0.375 or 37.5%.