Final answer:
The statement is false. According to the Empirical Rule, about 68 percent of observed values of a normally distributed variable lie within one standard deviation of the mean, while about 95 percent lie within two standard deviations.
Step-by-step explanation:
The statement concerning the proportion of values within two standard deviations of the mean in a normally distributed random variable is false. According to the Empirical Rule, approximately 68 percent of the observed values lie within one standard deviation of the mean. It is about 95 percent of the observed values that lie within two standard deviations of the mean. Applying this rule, for a normal distribution with a mean (μ) of 25 and a standard deviation (σ) of 5, about 95 percent of the values would lie within 15 to 35 (25 ± 2×5).
To illustrate this with an example, suppose a variable X has a normal distribution with a mean (50) and standard deviation (6). About 68 percent of the x values would be between 44 and 56, which corresponds to one standard deviation from the mean. Values between 38 and 62 would include about 95 percent of the x values, which is within two standard deviations of the mean.