# You take a sample of 144 observations and have a value of x bar equal to 59. The population mean is 68 and the population standard deviation is 36. What is the z score of your sample mean?

Jan 20, 2018

$- 3$

#### Explanation:

we use the standardising formula

$Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}$

we have

$\overline{X} = 59$

$\mu = 68$

$\sigma = 36$

$n = 144$

$\therefore Z = \frac{59 - 68}{\left(\frac{36}{\sqrt{144}}\right)} = - \frac{9}{\frac{36}{12}}$

$Z = - \frac{9}{3} = - 3$