Each trial of a certain lab procedure is scored 0 (total failure), 1 (marginal result), 2 (good result), or 3 (excellent result) according to the population distribution:

x 0 1 2 3
f(x) 0.1 0.2 0.4 0.3

Let 3 denote the sample mean score from two independent trials of this procedure.

What's the probability that X-bar will equal 1.5?

Answer: 0.22

Question

Each trial of a certain lab procedure is scored 0 (total failure), 1 (marginal result), 2 (good result), or 3 (excellent result) according to the population distribution:

 x          0          1          2          3
f(x)      0.1       0.2       0.4      0.3

Let 3 denote the sample mean score from two independent trials of this procedure.

What's the probability that X-bar will equal 1.5?

Answer: 0.22