The required interval of the given normal distribution using the empirical rule is <u>[100, 140]</u>.
The empirical rule formula (also known as a 68 95 99 rule formula) uses data from a normal distribution to determine the first, second, and third standard deviations, which, respectively, differ from the mean value by 68%, 95%, and 99%. Additionally, it shows that 99.9% of the data fall inside the third standard deviation range (either above or below the mean value). The empirical rule formula is described below with cases that have been resolved.
In the question, we are given that IQ scores for adults aged 20 to 34 years are normally distributed according to N(120, 20), and are asked for the range in which the middle 68% of people in this group score on the test.
N(120, 20) signifies a normal distribution with mean, μ = 120, and the standard deviation, σ = 20.
By the empirical formula, 68% of the data lies within one standard deviation from the mean.
Thus, the required interval is [μ - σ, μ + σ] = [120 - 20, 120 + 20] = [100, 140].
Learn more about the empirical rule at
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