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If a distribution of test scores is normal with a mean of 78 and a standard deviation of 11, calculate the z-score for the following scores X Z-score 60 70 80 90 60 65 70 80 99 89 75 Make sure to round up your answers to two digits after the decimal point.

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Answer:

Step-by-step explanation:

As we know z- score is defined by the formula [tex]z=\frac{x-\mu }{\sigma }[/tex]

Mean of the scores is given as 78 and standard deviation 11.

Now for x = 60

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

[tex]z=\frac{60-78}{11}=\frac{(-18)}{11}=-1.64[/tex]

For x = 70

[tex]z=\frac{70-78}{11}[/tex]

[tex]z=\frac{(-8)}{11}[/tex] =-0.73

For x = 80

[tex]z=\frac{80-78}{11}[/tex]

z = 0.18

For x = 90

[tex]z=\frac{90-78}{11}[/tex]

z = 1.09

For x = 60

z = -1.64

For x = 65

[tex]z=\frac{65-78}{11}[/tex]

z = -1.18

For x = 70

z = -0.73

For x = 80

z = 0.18

For x = 99

[tex]z=\frac{99-78}{11}[/tex]

z = 1.91

For x = 89

[tex]z=\frac{89-78}{11}[/tex]

z = 1

For x = 75

[tex]z=\frac{75-78}{11}[/tex]

z = -0.27

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