Question

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

Answer 1

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., $\mu$ = 500 and $\sigma$ = 100

The z score distribution is given by;

              Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where X represents the data values;

• So, z score for value 560 is;

                 z score = $\frac{560-500}{100}$ = 0.6

• So, z score for value 650 is;

                 z score = $\frac{650-500}{100}$ = 1.5

• So, z score for value 500 is;

                 z score = $\frac{500-500}{100}$ = 0

• So, z score for value 450 is;

                 z score = $\frac{450-500}{100}$ = -0.5

• So, z score for value 300 is;

                 z score = $\frac{300-500}{100}$ = -2