Answer :
The statement in question relates to the Empirical Rule, which is used to summarize data with a normal distribution. This rule is often referred to as the 68-95-99.7 rule. Let's break it down:
Normal Distribution: It's a continuous probability distribution that is symmetrical around its mean, meaning most of the observations cluster around the central peak and the probabilities for values further off the mean taper off equally in both directions.
Empirical Rule (68-95-99.7 Rule): This rule states that for a normal distribution:
- About 68% of the data falls within one standard deviation (σ) of the mean (μ).
- About 95% of the data falls within two standard deviations (2σ) of the mean (μ).
- About 99.7% of the data falls within three standard deviations (3σ) of the mean (μ).
The statement is asking if approximately 95% of the values are within standard deviations of the mean. Specifically, the statement seems to imply two standard deviations here, which aligns with the part of the empirical rule stating that about 95% of data falls within two standard deviations.
Thus, the statement given is True. The assertion correctly matches the portion of the Empirical Rule describing that 95% of values in a normal distribution lie within two standard deviations from the mean.
