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ankoles [38]
3 years ago
13

Range of scores making up the interquartile ranger

Mathematics
1 answer:
Nostrana [21]3 years ago
4 0

For a standard normally distributed random variable <em>Z</em> (with mean 0 and standard deviation 1), we get a probability of 0.0625 for a <em>z</em>-score of <em>Z</em> ≈ 1.53, since

P(<em>Z</em> ≥ 1.53) ≈ 0.9375

You can transform any normally distributed variable <em>Y</em> to <em>Z</em> using the relation

<em>Z</em> = (<em>Y</em> - <em>µ</em>) / <em>σ</em>

where <em>µ</em> and <em>σ</em> are the mean and standard deviation of <em>Y</em>, respectively.

So if <em>s</em> is the standard deviation of <em>X</em>, then

(250 - 234) / <em>s</em> ≈ 1.53

Solve for <em>s</em> :

16/<em>s</em> ≈ 1.53

<em>s</em> ≈ 10.43

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