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

1.2

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

Explanation:

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

The formula to find the z-value :-

`z=(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=(x-\mu)/(\sigma)\\\\\Rightarrow\ 1.2=(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.