Question

A2 Statistics Practice (I need help solving questions 5-7)

Answer 1

5. Given a specific value of $X$, the corresponding $Z$ value is obtained from

$Z=\dfrac{X-\mu_X}{\sigma_X}$

You're given $\sigma_X=17$ and that $z=-1.5$ when $x=250$. This means

$-1.5=\dfrac{250-\mu_X}{17}\implies\mu_X=275.5$

6. Same as 3 and 4. I assume you have a calculator you can use to find $P(z$. 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

$18.72=31.5-1.5\sigma_X\implies\sigma_X=8.52$