Answer:
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%.