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Consider the following scores. (i) a score of 40 from a distribution with mean 50 and standard deviation 10 (ii) a score of 45 from a distribution with mean 50 and standard deviation 5 How do the two scores compare relative to their respective distributions

1 Answer

1 vote

Answer:

The scores are equal

Explanation:

The z-score for any normal distribution is:


z=(X-\mu)/(\sigma)

(i) Score (X) = 40

Mean (μ)= 50

Standard deviation (σ) = 10


z=(40-50)/(10)\\ z=-1

(ii) Score (X) = 45

Mean (μ)= 50

Standard deviation (σ) = 5


z=(45-50)/(5)\\ z=-1

Both scores have the same z-score, which means that, relative to their respective distributions, the scores are equal.

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