Question

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.

Answer 1

Answer:

Step-by-step explanation:

As we know z- score is defined by the formula $z=\frac{x-\mu }{\sigma }$

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

Now for x = 60

$z=\frac{x-\mu }{\sigma }$

$z=\frac{60-78}{11}=\frac{(-18)}{11}=-1.64$

For x = 70

$z=\frac{70-78}{11}$

$z=\frac{(-8)}{11}$ =-0.73

For x = 80

$z=\frac{80-78}{11}$

z = 0.18

For x = 90

$z=\frac{90-78}{11}$

z = 1.09

For x = 60

z = -1.64

For x = 65

$z=\frac{65-78}{11}$

z = -1.18

For x = 70

z = -0.73

For x = 80

z = 0.18

For x = 99

$z=\frac{99-78}{11}$

z = 1.91

For x = 89

$z=\frac{89-78}{11}$

z = 1

For x = 75

$z=\frac{75-78}{11}$

z = -0.27