Final answer:
The probability that a normal variable X lies within 2 standard deviations of its mean is about 95%, or 0.9544, according to the empirical rule.
Step-by-step explanation:
The question asks for the probability that a normally distributed continuous random variable X lies within 2 standard deviations (σ) of its mean (μ). This is known as applying the empirical rule or the 68-95-99.7 rule, which states that for a normal distribution, approximately 68% of data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% within three standard deviations.
Thus, the probability P(μ−2σ < X < μ+2σ) is about 95%, or more specifically, about 0.9544. This means the correct answer to the question would be about .9544, reflecting the portion of the distribution that lies within this range.