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Normal Distribution: 68-95-99.7 Rule, Confidence Interval

1. The Environmental Protection Agency (EPA) fuel economy estimates for automobiles tested recently predicted
a mean of 24.8 mpg with a standard deviation of 6.2 mpg for highway driving. Assume that the data is normally distributed. Using the 68-95-99.7 Rule, Determine:

a. Within what interval you would expect the middle 68% of the autos gas mileages to be found?
b. What percent of the autos should get more than 31 mpg?
c. What percent of the autos should get between 31 and 37.2 mpg?
d. What percent of the autos would you expect to get less than 18.6 mpg?
e. What percent of the autos would have a gas mileage of no more than 12.4 mpg
f. What is the gas mileage of the worst 2.5% of the autos?

2. A forester measured 27 of the trees in a large forest that is to be sold. He found that mean diameter of the 27
trees was 10.4 inches with a standard deviation of 4.7 inches. Suppose that this group of trees provides an accurate description of the trees in the whole forest and that the distribution of the tree diameters is Normal.

a. What are the limits within which you would expect to find the middle 95% of the tree diameters?
b. What percent of the trees would have a diameter of 1 inch or less?
c. What percent of the trees would have a diameter between 5.7 and 10.4 inches?
d. What percent of the trees would be over 15 inches in diameter?
e. What percent of the trees would be less than 10.4 inches in diameter?

Solution Preview

1. The Environmental Protection Agency (EPA) fuel economy estimates for automobiles tested recently predicted a mean of 24.8 mpg with a standard deviation of 6.2 mpg for highway driving. Assume that the data is normally distributed. Using the 68-95-99.7 Rule, Determine:

Mean=Mu = 24.80 mpg
Standard deviation =s= 6.20 mpg

a. Within what interval you would expect the middle 68% of the autos gas mileages to be found?

Mu +s= 31.00 mpg =24.8+6.2
Mu -s= 18.60 mpg =24.8-6.2

Answer: 18.60 mpg to 31.00 mpg

b. What percent of the autos should get more than 31 mpg?

% beyond Mu +s= ...

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