Answer:
83.85% of 1-mile long roadways with potholes numbering between 57 and 89
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed(bell-shaped) random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 65
Standard deviation = 8
Using the empirical (68-95-99.7) rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 57 and 89?
It is important to remember that the normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are avobe.
57 = 65 - 8
So 57 is one standard deviation below the mean.
By the Empirical Rule, 68% of the 50% below the mean is within 1 standard deviation of the mean.
89 = 65 + 3*8
So 89 is three standard deviations above the mean.
By the Empirical Rule, 99.7% of the 50% above the mean is within 3 standard deviations of the mean.
0.68*0.5 + 0.997*0.5 = 0.8385
83.85% of 1-mile long roadways with potholes numbering between 57 and 89