Answer to Question #297627 in Statistics and Probability for Klong

Question

Given 𝑥 ̅ = 62 and s = 8. Find the z-score value that corresponds to each of the following scores up to two decimal places.

X=70

X=78

X=82

X=50

X=42

Answer 1

Solution :

Given that ,

mean = $\mu$  = 62

standard deviation = $\sigma$  = 8

1) x = 70

Using z-score formula,

z = $\dfrac{x-\mu}{\sigma}$     

z = (70 - 62) / 8

z = 1.00

2) x = 78

Using z-score formula,  

z = (78 - 62) / 8

z = 2.00

3) x = 82

Using z-score formula, 

z = (82 - 62) / 8

z = 2.50

4) x = 50

Using z-score formula,  

z = (50 - 62) / 8

z = -1.50

5) x = 42

Using z-score formula, 

z = (42 - 62) / 8

z = -2.50