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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

Verified Answer :

\(18=12+4x\implies 6=4x\implies x=\dfrac64=1.5\)

Answer:

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

Step-by-step 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

\(z=\frac{x-\mu}{\sigma}\)

The value of x is 18.

\(z=\frac{18-12}{4}\)

\(z=\frac{6}{4}\)

\(z=1.5\)

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.