Suppose a Normal model describes the fuel efficiency of cars currently registered on your state. The mean is 24 mpg, with a standard deviation of 6 mpg.
-Describe the fuel efficiency of the worst 20% of all cars.
I know that you convert 20% into decimal form to get .2 and put that number in for Invnorm to get -.84, but how do I get the fuel efficiency of the worst 20% of cars from there.
I don't have a normal curve or a chart handy, so I will trust that your value of -.84 for .2 is correct.
What that means is that 20% lies from the point .84 of a standard deviation to the left of the mean.
.84(6)=5.04
so 20% of the cars will have a fuel efficiency of below 18.96 mpg
To find the fuel efficiency of the worst 20% of cars, you can use the Z-score and the standard deviation of the Normal distribution.
First, find the Z-score that corresponds to the 20th percentile (or the worst 20%) by using the InvNorm function in your calculator or statistical software. In this case, you correctly stated that the Z-score for a 20% percentile is -0.84.
Next, multiply the Z-score by the standard deviation of the model. In this case, the standard deviation is 6 mpg. So, -0.84 multiplied by 6 gives you -5.04.
Finally, subtract the result from the mean of the model to find the fuel efficiency of the worst 20% of cars. In this case, the mean is 24 mpg. So, 24 minus 5.04 equals approximately 18.96 mpg.
Therefore, the fuel efficiency of the worst 20% of cars is approximately 18.96 mpg.