Question

If the mileage per gallon for a car is normally distributed, 32 mpg has a z score of 1.2, and 24 mpg, has a z score of -.4, what is the mean mpg of the distribution?

Answer 1

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.