Chapter 6 Worksheet 1 Solutions

AP Statistics
Chapt. 6 Wksht
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Name__Solutions_______________
Date_________________________

Answer the following questions from the given situation.
Suppose a Normal model describes the fuel efficiency of cars currently registered in your state.
The mean is 24 mpg, with a standard deviation of 6 mpg.
-3σ - 2σ -1σ μ 1σ 2σ 3σ
1. Sketch the Normal model (label).
68%
95%
99.7
%

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2. What percent of cars get less than 15 mpg?
15  24 z  1.5 P(y<15)=P(z<-1.5)=6.7%
6 12 18 24 30 36 42
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3. What percent of cars get between 20 and 30 mpg?
20  24
30  24
P(20<y<30)=P(-0.67<z<1)=58.8%
z
 .67 z 1
6
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4. What percent of cars get more than 40 mpg?
40  24 z  2.67 P(y>40)=P(z>2.67)=0.4%
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5. What gas mileage represents the third quartile? y  24
Q375%  using invnorm(.75) gives z=0.674  0.674 
 y = 28 mpg
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6. Describe the gas mileage of the most efficient 5% of all cars. y  24
That corresponds to 95% to the leftinvnorm(.95) gives 1.64  1.64 
 y = 34 mpg
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Consider the fuel economy model to be N(24,6). Sketch pictures as you answer these questions.
7. Describe the fuel efficiency of the worst 10% of all cars. y  24
An area of 10% corresponds to z = -1.28
 1.28 
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y = 16.3 mpg

8. An ecology group is lobbying for a national goal calling for no more than 10% of all cars to be under 20 mpg. If the standard deviation doesn’t change, what average fuel efficiency must be attained? 20  
 1.28 
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μ = 27.7 mpg
9. Car manufacturers argue that they cannot raise the average that much. They believe they can only get 26 mpg. What standard deviation would allow them to meet the “only 10% under 20 mpg” goal?
20  26
 1.28 

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μ = 4.7 mpg