The difference in gallons per day used is 3.6.
The formula to calculate a z-score is:
[tex]z=\frac{X-\mu}{\sigma}[/tex],
where X is the value used to calculate the score, μ is the mean and σ is the standard deviation. We have the z-scores so we must work backward:
[tex]3=\frac{X-2.2}{1.2}\text{ and }0=\frac{X-2.2}{1.2}[/tex]
For both equations, we will cancel the 1.2 by multiplying both sides:
[tex]3\times1.2=(\frac{X-2.2}{1.2})\times1.2\text{ and }0\times1.2=(\frac{X-2.2}{1.2})\times1.2
\\
\\3.6=X-2.2\text{ and }0=X-2.2[/tex]
Now we will cancel 2.2 from both equations by adding it to both sides:
3.6+2.2=X-2.2+2.2 and 0+2.2=X-2.2+2.2
5.8=X and 2.2=X
The difference in gas used per day would be given by
5.8-2.2 = 3.6.
