Question

A normal distribution of data has a mean of 15 and a standard deviation of 4. How many standard deviations from the

mean is 25?

Answer 1

2.5

Explanation:

i just took the test

Answer 2

25 is 2.5 standard deviations from the mean.

Explanation:

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean.

In this question:

Mean of 15 and a standard deviation of 4, so
`\mu = 15, \sigma = 4`

How many standard deviations from the mean is 25?

We have to find Z when
`X = 25`. So

`Z = (X - \mu)/(\sigma)`

`Z = (25 - 15)/(4)`

`Z = 2.5`

So 25 is 2.5 standard deviations from the mean.