Question

Suppose a normal distribution has a mean of 20 and a standard deviation of four. A value of 26 is how many standard deviation's away from the mean?

Answer 1

$26=20+6=20+\dfrac64\times4=20+1.5\times4$

which means 26 is 1.5 standard deviations away from the mean.

Answer 2

Knowing that:
The standard score, or z-score, represents the number of Standard deviations that separate a random variable x from average.

Formula:

$z = \frac{value-average}{standard\:deviation}$

Data:
z = ?
value = 26
average = 20
standard deviation = 4

Solving:


$z = \frac{value-average}{standard\:deviation}$

$z = \frac{26-20}{4}$
$z = \frac{6}{4}$
$\boxed{\boxed{z = 1.5}} \end{array}}\qquad\quad\checkmark$

Answer:
$\underline{26\:is\:1.5\:standard\:deviation\:in\:relation\:to\:the\:average.}$