5. Given a specific value of [tex]X[/tex], the corresponding [tex]Z[/tex] value is obtained from
[tex]Z=\dfrac{X-\mu_X}{\sigma_X}[/tex]
You're given [tex]\sigma_X=17[/tex] and that [tex]z=-1.5[/tex] when [tex]x=250[/tex]. This means
[tex]-1.5=\dfrac{250-\mu_X}{17}\implies\mu_X=275.5[/tex]
6. Same as 3 and 4. I assume you have a calculator you can use to find [tex]P(z<2.25)[/tex]. You should get around 0.9878.
7. We're told that 18.72 is 1.5 standard deviations below the mean of 31.5. This translates to
[tex]18.72=31.5-1.5\sigma_X\implies\sigma_X=8.52[/tex]
