Final answer:
The standard deviation of a uniformly distributed random variable X between 2 and 12 is approximately 2.887, calculated using the formula σ = √((b - a)² / 12). This corresponds to option d.
Step-by-step explanation:
The random variable X is known to be uniformly distributed between a lower limit a = 2 and an upper limit b = 12. The formula for the standard deviation (σ) of a uniform distribution is σ = √((b - a)2 / 12). Substituting the given limits into the formula, we get:
σ = √((12 - 2)2 / 12)
σ = √(100 / 12)
σ = √(8.333)
σ ≈ 2.887
Therefore, the standard deviation of X is approximately 2.887, which corresponds to option d.