The range of scores for 95% of the class is 63.8 to 86.6 using the empirical rule.
A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will lie within three standard deviations.
The empirical rule specifically states that 68 percent of data will fall inside the first standard deviation, 95 percent will fall within the first two standard deviations, and 99.7 percent will fall within the first three standard deviations.
According to the question,
μ=75.2 and σ=5.7
So, according to the empirical rule, the range of scores for 95% of the class:
μ – 2σ =75.2-2*5.7=63.8
and μ + 2σ=75.2+2*5.7=86.6
Learn more about the empirical rule here:
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