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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?

Respuesta :

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

Then
[tex]z-score= \frac{1750-1500}{150} [/tex]
[tex]z-score=1.7[/tex] (rounded to one decimal place)

Answer:

The z-score is 1.667. ( approx )

Step-by-step explanation:

In normal distribution,

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

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Where,

[tex]\mu[/tex] is mean,

[tex]\sigma[/tex] is standard deviation,

Here,

[tex]\mu = 1500[/tex]

[tex]\sigma = 150[/tex]

Hence, the z-score of 1750 points is,

[tex]z=\frac{1750-1500}{150}[/tex]

[tex]=\frac{250}{150}[/tex]

[tex]\approx 1.667[/tex]

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