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+\frac64*4=20+1.5*4`

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 = (value-average)/(standard\:deviation)`

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

Solving:



`z = (value-average)/(standard\:deviation)`


`z = (26-20)/(4)`

`z = (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.}`