Question

Suppose you have a mean standardized score of 1500 points with a standard deviation of 150 points. This data is normally distributed. What is the z-score of 1750 points?

Answer 1

The z-score is 1.667. ( approx )

Explanation:

In normal distribution,

The z-score or standard score of a score x is,

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

Where,

`\mu` is mean,

`\sigma` is standard deviation,

Here,

`\mu = 1500`

`\sigma = 150`

Hence, the z-score of 1750 points is,

`z=(1750-1500)/(150)`

`=(250)/(150)`

`\approx 1.667`

Answer 2

Mean, μ=1500
Standard Deviation, σ=150
X=1750

Then

`z-score= (1750-1500)/(150)`

`z-score=1.7` (rounded to one decimal place)