Question

A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was 14781478 and the standard deviation was 311311. The test scores of four students selected at random are 18701870​, 12001200​, 21802180​, and 13801380. Find the​ z-scores that correspond to each value and determine whether any of the values are unusual.

Answer 1

Answer:

Z SCORE FOR 1870 = 1.26

Z SCORE FOR 1200 = -0.89

Z SCORE FOR 2180 = 2.25

Z SCORE FOR 1380 = -0.315

Step-by-step explanation:

given data:

test score $\mu$ = 1478

standard deviation $\sigma$ = 311

z score can be calculated by using below relation

$Z = \frac{X-\mu}{\sigma}$

1) Z SCORE FOR 1870

$= \frac{1870-1478}{311}$

= 1.26

2) Z SCORE FOR 1200

$= \frac{1200-1478}{311}$

= -0.89

3) Z SCORE FOR 2180

$= \frac{2180-1478}{311}$

= 2.25

4) Z SCORE FOR 1380

$= \frac{1380-1478}{311}$

= -0.315

There are no unusual z value.