Question

Mrs. Miller's statistics test scores are normally distributed with a mean score of 85 (μ) and a standard deviation of 5 (σ). Using the Empirical Rule, about 95% of the scores lie between which two values? Provide your answer below: 95% of the x- values lie between _ and_

Answer 1

Mean = μ = 85

Standard deviation = σ = 5

The empirical rule states that for a normal distribution, almost all data will fall within three standard deviations of the mean. It shows that 68% will fall within the first standard deviation, 95% within the first two standard deviations, and 99.7% will fall within the first three standard deviations of the distribution's average.

μ + 2*σ = 85 + 2*5 = 95

μ - 2*σ = 85 - 2*5 = 75

95% of the x- values lie between 75 and 95.