A standardized exams scores are normally distributed In a re

A standardized exam\'s scores are normally distributed. In a recent year, the mean test score was 1498 and the standard deviation was 311. The test scores of four students selected at random are 1910,1250, 2230, and 1400. Find the z-scores that correspond to each value and determine whether any of the values are unusual.

Solution

A score is rare if |z| > 2.

As

z = (x-u)/sigma

then for x = 1910:

z = (1910-1498)/311 = 1.324758842 [not rare]

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for x = 1250:

z = (1250-1498)/311 = -0.797427653 [not rare]

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for x = 2230:

z = (2230-1498)/311 = 2.353697749 [rare]

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for x = 1400:

z = (1400-1498)/311 = -0.31511254 [not rare]