Question

An urn contains exactly three balls numbered 1, 2, and 3, respectively. Random samples of two balls are drawn from the urn with replacement. The average, xbar=(x1+x2)/2 , where X1 and X2 are the numbers on the selected balls, is recorded after each drawing. Which of the following describes the sampling distribution of xbar? (A) xbar 1 1.5 2 2.5 3 Prob. 1/5 1/5 1/5 1/5 1/5 (B) xbar 1 1.5 2 2.5 3 Prob. 1/9 2/9 1/3 2/9 1/9 (C) xbar 1 1.5 2 2.5 3 Prob. 0 0 1 0 0 (D) xbar 1 1.5 2 2.5 3 Prob. 1/10 1/10 1/10 1/10 1/10 (E) It cannot be determined from the information given.

Answer 1

The sampling distribution of xbar can be determined by considering the probabilities of obtaining each possible value of xbar. In this case, the random samples of two balls are drawn from the urn with replacement. The sampling distribution of xbar is given by xbar: 1, 1.5, 2, 2.5, 3 and the corresponding probabilities are 1/9, 2/9, 1/9, 2/9, and 1/9, respectively.

Step-by-step explanation:

The sampling distribution of xbar can be determined by considering the probabilities of obtaining each possible value of xbar. In this case, the random samples of two balls are drawn from the urn with replacement. The average, xbar=(x1+x2)/2, where X1 and X2 are the numbers on the selected balls, is recorded after each drawing.

There are a total of 3*3=9 possible pairs of balls that can be drawn. The sums of the pairs are 2, 3, 4, 3, 4, 5, 4, 5, and 6. The corresponding probabilities are 1/9, 2/9, 1/9, 2/9, 1/9, 2/9, 1/9, 2/9, and 1/9, respectively.

Therefore, the sampling distribution of xbar is given by xbar: 1, 1.5, 2, 2.5, 3 and the corresponding probabilities are 1/9, 2/9, 1/9, 2/9, and 1/9, respectively. The correct answer is (B).