Hi there!
We can use the following equation:
[tex]\large\boxed{z = \frac{x-\mu}{\sigma}}[/tex]
z = amount of standard deviations away a value is from the mean (z-score)
σ = standard deviation
x = value
μ = mean
Plug in the knowns for both and rearrange to solve for the mean:
[tex]-1 = \frac{19-\mu}{\sigma}\\\\-\sigma = 19 - \mu\\\\ \sigma = -19 + \mu[/tex]
Other given:
[tex]2 = \frac{40-\mu}{\sigma}\\\\2\sigma = 40- \mu\\\\ \sigma = 20 - \frac{\mu}{2}[/tex]
Set both equal to each other and solve:
[tex]-19 + \mu = 20 - \frac{\mu}{2}\\\\\frac{3\mu}{2} = 39 \\\\3\mu = 78 \\\\\boxed{\mu = 26 }[/tex]
