10) A competency test has scores with a mean of 255 and a standard deviation of 61. A histogram of the data shows that the distribution is
normal. Use the Empirical Rule to find the percentage of scores higher than 72

The percentage of scores higher than 72 is 99.85%

Explanation:

The empirical rule states that about 68% of observations falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ)

We can use the relationship below

255-σ(61)=72

61σ=255-72

61σ=183

σ=3

The area is as shaded below

The percentage of scores higher than 72 is 99.7%+0.15%=99.85%