Question

Suppose a normal distribution has a mean of 12 and a standard deviation of 4.

A value of 18 is how many standard deviations away from the mean?

-2
-1.5
1.5
2

Answer 1

`18=12+4x\implies 6=4x\implies x=\frac64=1.5`

Answer 2

The correct option is 3. The value of 18 is 1.5 standard deviations away from the mean.

Explanation:

It is given that a normal distribution has a mean of 12 and a standard deviation of 4.

`\mu=12`

`\sigma=4`

We have to find the value of

`z=(x-\mu)/(\sigma)`

The value of x is 18.

`z=(18-12)/(4)`

`z=(6)/(4)`

`z=1.5`

The value of z is 1.5, therefore the value of 18 is 1.5 standard deviations away from the mean. Option 3 is correct.