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?

  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.

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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if x = 1, then the answer is 3.5