A. Its mean is 2.7 (rounded to the nearest tenth).
To determine whether the table is a probability distribution, we need to check two conditions:
The probabilities must be non-negative: P(x) ≥ 0 for all x.
The sum of all probabilities must be equal to 1: Σ P(x) = 1 over all possible values of x.
Let's check these conditions:
All probabilities in the given table are non-negative, so the first condition is satisfied.
Summing up the probabilities:
0.05 + 0.12 + 0.28 + 0.27 + 0.17 + 0.11 = 1.00
Both conditions are satisfied, so the table is a probability distribution.
Now, to find the mean (μ) of the probability distribution, you can use the formula:
μ=∑i xi ⋅ P(xi )
where xi is the value of the random variable, and P(xi ) is the probability of xi.
μ=(0⋅0.05)+(1⋅0.12)+(2⋅0.28)+(3⋅0.27)+(4⋅0.17)+(5⋅0.11)
μ=0+0.12+0.56+0.81+0.68+0.55
μ=2.72
So, the mean of the probability distribution is 2.72 (rounded to the nearest tenth).
Therefore, the correct choice is:
A. Its mean is 2.7 (rounded to the nearest tenth).