Question

A given data value has a Z-value equal to 1.2. Assuming a normal (i.e., symmetrical) continuous probability distribution, how many standard deviations is the data value from the mean?

Answer 1

Answer:

1.2

Step-by-step explanation:

the number of standard deviations that the data value is away from the mean is 1.2 standard deviations, and thats because the units of the Z values are standard deviations.

if you remember the Z value formula is (X - mean) / SD, you are subtracting the X (data value) from the mean, and then dividing by standard deviations to get the number of standard deviations that the data value is away from the mean

if the Z value is positive that means that the data value is above from the mean.

if the Z value is negative that means that the data value is below from the mean

Answer 2

Answer:  1.2

Step-by-step explanation:

Let x  be a random data value that follows a normal distribution.

The formula to find the z-value :-

$z=\dfrac{x-\mu}{\sigma}$, where $\mu$ is the population mean and $\sigma$ is the standard deviation.

Given : A  data value has a Z-value equal to 1.2.

Then, we have

$z=\dfrac{x-\mu}{\sigma}\\\\\Rightarrow\ 1.2=\dfrac{x-\mu}{\sigma}\\\\\Rightarrow\ x-\mu=1.2\sigma\\\\\Rightarrow\ x=\mu+1.2\sigma$

Hence, the  data value is 1.2 standard deviations from the mean.