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sergiy2304 [10]
3 years ago
9

In its Fuel Economy Guide for 2016 model vehicles, the Environmental Protection Agency gives data on 1170 vehicles. There are a

number of high outliers, mainly hybrid gas‑electric vehicles. If we ignore the vehicles identified as outliers, however, the combined city and highway gas mileage of the other 1146 vehicles is approximately Normal with mean 23.0 miles per gallon (mpg) and standard deviation 4.9 mpg.
The quartiles of any distribution are the values with cumulative proportions 0.25 and 0.75. They span the middle half of the distribution.
a. What is the first quartile of the distribution of gas mileage?
b. What is the third quartile of the distribution of gas mileage?
Mathematics
1 answer:
Nady [450]3 years ago
5 0

Answer:

a. 19.68 miles per gallon.

b. 26.32 miles per gallon.

Step-by-step explanation:

Mean gas mileage (μ) = 23.0 mpg

Standard deviation (σ) = 4.9 mpg

In a normal distribution, for any length X, the z-score is determined by the following expression:

 z=\frac{X-\mu}{\sigma}

In a normal distribution, the 25th percentile  (first quartile) of a normal distribution has a corresponding z-score of z = -0.677 and the 75th percentile  has a corresponding z-score of z = 0.677

a. The first quartile of the distribution of gas mileage is

-0.677=\frac{X_{25}-23}{4.9}\\X_{25}=19.68\ mpg

19.68 miles per gallon.

b. The third quartile of the distribution of gas mileage is

0.677=\frac{X_{25}-23}{4.9}\\X_{25}=26.32\ mpg

26.32 miles per gallon.

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Maggie’s brother is 6 years younger than three times her age. The sum of their ages is 42. How old is Maggie?
GarryVolchara [31]
X = Maggie's age

y = The brother's age

x + y = 42

y = 3x - 6

Using the substitution property, we can replace y in the first equation with the 3x - 6 in the second equation like so:

x + (3x - 6) = 42

Then solve this equation for x like so:

x + (3x - 6) = 42

x + 3x = 48 (Add 6 to both sides)

4x = 48 (Simplify)

x = 12 (Divide both sides by 4)

This shows that Maggie's is 12 years old. In order to prove this, you must check your work. In order to do this, first plug your answer back into the original equation like so:

x + y = 42

12 + y = 42. (Plug in answer)

y = 30 (Subtract both sides by 12)

This shows that Maggie's brother is 30 years old. The final step to proving this is to plug both of your answers into the second equation to make sure that your answers are within the constraints set by the problem. Do this like so:

y = 3x - 6

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Because the equation is balanced, your answers are correct. So, to answer your question, Maggie is 12 years old.


4 0
3 years ago
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