Concept explainers
a)
To draw the model which shows 68-95-99.7
a)
Explanation of Solution
Given:
Following is the model which shows 68-95-99.7:
b)
To find the interval in which 68% of autos to be found.
b)
Answer to Problem 25E
The central 68% of autos can be found between 18.6 mpg and 31.0 mpg
Explanation of Solution
Given:
According to rule of 68-95-99.7, the 68% of the values are within 1 standard deviation of the mean.
Therefore,
Hence, the central 68% of autos can be found between 18.6 mpg and 31.0 mpg.
c)
To find the percent of autos should get more than 31 mpg.
c)
Answer to Problem 25E
The 16% of autos should get more than 31 mpg.
Explanation of Solution
Given:
The central 68% of autos can be found between 18.6 mpg and 31.0 mpg.
According to rule, 31 is 1 standard deviation above the mean. Therefore, when data is in total 100%, 32% of the data is then more than 1 standard deviation from the mean. We know, the normal curve is symmetric about the mean then 16% is more than 1 standard deviation below the mean and 16% is more than 1 standard deviation above the mean. So, we can say, 16% of autos should get more than 31 mpg.
d)
To find the percent of cars should bet between 31 and 37.2 mpg
d)
Answer to Problem 25E
The 13.5% of cars should get between 31 and 37.2 mpg.
Explanation of Solution
Given:
According to rule, 31 is 1 standard deviation above the mean. As per graph,37.2 is 2 standard deviation above the mean. Therefore, 95%-68% = 27% which is more than 1 standard deviation and less than 2 standard deviation of the mean. We know, the normal curve is symmetric about the mean then 13.5% is more than 1 standard deviation but less than 2 standard deviation below the mean and 13.5% is more than 1 standard deviation but less than 2 standard deviationabove the mean. So, we can say, 13.5% of cars should get between 31 and 37.2 mpg.
e)
To explain the gas mileage of the worst 2.5% of all cars.
e)
Answer to Problem 25E
The worst 2.5% have a gas mileage less than 12.4 mpg.
Explanation of Solution
Given:
According to rule, 95% of the data lies between 2 standard deviations from the mean. Since, total data is 100%, so 5% of the data is the more than 2 standard deviations from the mean. Therefore, as per symmetry, 2.5% is more than 2 standard deviations below the mean and 2.5% is more than 2 standard deviations above the mean.
Therefore, the worst 2.5% have a gas mileage less than 12.4 mpg.
Chapter 6 Solutions
Stats: Modeling the World Nasta Edition Grades 9-12
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (4th Edition)
Elementary Statistics: Picturing the World (7th Edition)
Calculus: Early Transcendentals (2nd Edition)
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