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Consider a sample with a mean of 500 and a standard deviation of 100. What are the z-scores for the following data values: 560, 650, 500, 450, and 300? z-score for 560 z-score for 650 z-score for 500 z-score for 450 z-score for 300

Respuesta :

Answer:

z-score for value 560 = 0.6

z-score for value 650 = 1.5

z-score for value 500 = 0

z-score for value 450 = -0.5

z-score for value 300 = -2

Step-by-step explanation:

We are given a sample with a mean of 500 and a standard deviation of 100.

i.e., [tex]\mu[/tex] = 500 and [tex]\sigma[/tex] = 100

The z score distribution is given by;

              Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)

where X represents the data values;

  • So, z score for value 560 is;

                 z score = [tex]\frac{560-500}{100}[/tex] = 0.6

  • So, z score for value 650 is;

                 z score = [tex]\frac{650-500}{100}[/tex] = 1.5

  • So, z score for value 500 is;

                 z score = [tex]\frac{500-500}{100}[/tex] = 0

  • So, z score for value 450 is;

                 z score = [tex]\frac{450-500}{100}[/tex] = -0.5

  • So, z score for value 300 is;

                 z score = [tex]\frac{300-500}{100}[/tex] = -2

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