if michaels score is 87, the class average is 82, and the standard deviation is 4. what is michaels z-score?

Mathematics

1 answer:

AlexFokin [52]2 years ago

3 0

Answer:

Z = 1.25

Step-by-step explanation:

$\displaystyle Z=\frac{\text{Observed Value}-\text{Mean of the Sample}}{\text{Standard Deviation of the Sample}}\\\\Z=\frac{x-\mu}{\sigma}\\ \\Z=\frac{87-82}{4}\\ \\Z=\frac{5}{4}\\ \\Z=1.25$

Hence, Michael's z-score is 1.25, which means that he scored 1.25 standard deviations above the class average.

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Free_Kalibri [48]

QUESTION 1

We want to solve,

$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x^{2}-6x+8}$

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$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x(x-4) - 2(x - 4)}.$

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${x}^{2} + x - 4x - 2 - 2 = 0$

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${x}^{2} + - 3x - 4 = 0$

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${x}^{2} + x - 4x- 4 = 0$

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QUESTION 2

$\sqrt{x+11} -x=-1$

We add x to both sides,

$\sqrt{x+11} =x-1$

We square both sides,

$x + 11 = (x - 1)^{2}$

We expand to get,

$x + 11 = {x}^{2} - 2x + 1$

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$x = - 2 \: or \: x = 5$

But
$x = - 2$
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