(Solution) - Consider the population described by the probability distribution shown below The -(2025 Original AI-Free Solution)

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Consider the population described by the probability distribution shown below.

The random variable x is observed twice. If these observations are independent, verify that the different samples of size 2 and their probabilities are as shown in the next column.

a. Find the sampling distribution of the sample mean
b. Construct a probability histogram for the sampling distribution of .
c. What is the probability that is 4.5 or larger?
d. Would you expect to observe a value of equal to 4.5 or larger? Explain.