Answer:
26 mpg
Step-by-step explanation:
The given numbers let you write two equations using the relation ...
z = (x - μ)/σ
Filling in the numbers, we have ...
1.2 = (32 - μ)/σ
-0.4 = (24 - μ)/σ
Dividing the first equation by the second gives ...
-3 = (32 -μ)/(24 -μ)
-3(24 -μ) = 32 -μ . . . . . multiply by the denominator
-72 +3μ = 32 -μ . . . . . eliminate parentheses
4μ = 104 . . . . . . . . . . . . add 72+μ
μ = 26 . . . . . . . . . . . . . . divide by 4
The mean of the distribution was 26 mpg.
The mean of the distribution of the mileage per gallon for the car is 26
The given parameters are:
The z-score of a distribution is:
[tex]z = \frac{x - \bar x}{\sigma}[/tex]
So, we have the following equations
[tex]1.2 = \frac{32 - \bar x}{\sigma}[/tex]
and
[tex]-4 = \frac{24 - \bar x}{\sigma}[/tex]
Divide both equations
[tex]-3 = \frac{32 - \bar x}{24- \bar x}[/tex]
Cross multiply
[tex]-72 + 3\bar x = 32 - \bar x[/tex]
Collect like terms
[tex]\bar x + 3\bar x = 32 + 72[/tex]
[tex]4\bar x = 104[/tex]
Divide both sides by 4
[tex]\bar x = 26[/tex]
Hence, the mean of the distribution is 26
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