Answer:
The mean of X, μₓ is 2
The standard deviation of X, σₓ is 1.3
Step-by-step explanation:
Here we have the expected value given by the following relation
Expected value = P(x) × n
Where:
P(x) = Probability that the event occurs
n = Number of times the event occurs
The probability of the dice showing 1 = 1/6
The number dice rolled = 12
Therefore, out of 12, the expected number of dice that show 1 in a turn = 12×1/6 = 2
The proportion, p of dice that show 1 = 1/6, hence the mean, μx = np
Standard deviation of a proportion, [tex]\sigma _x =\sqrt{np{(1 - p)} }[/tex]
Where:
p = 1/6
n = 12
Hence;
μx = 12 × 1/6 = 2
[tex]\sigma _x =\sqrt{np{(1 - p)} } = \sqrt{12 \times \frac{1}{6} (1 - \frac{1}{6}) } = \sqrt{\frac{5}{3} } = 1.29099 \approx 1.3 \ to \ the \ nearest \ tenth[/tex]
Hence the mean and standard deviation of X are presented as follows;
The mean of X, μₓ = 2
The standard deviation of X, σₓ = 1.3.
