Question

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

Answer 1

Answer:

The following are the solution to this question:

Step-by-step explanation:

In the given question, some of the values are missing which is defined in the attached file please find it.

In this question, the data is used to represent a standardized​ exam's scores, which is normally spread out into the test score that is  1530 and its standard deviation 316.  

Formula:

$\to z=\frac{X- \mu}{\sigma }$

If the value of z-score= 1930

       $\to z =\frac{1930- 1530}{316 } \\\\ \to z =\frac{400}{316 } \\\\ \to z = 1.27$

The z-score is 1.27

If the value of z-score= 1250

       $\to z =\frac{1250- 1530}{316 } \\\\ \to z =\frac{-280}{316 } \\\\ \to z = -0.886$

The z-score is -0.886

If the value of z-score= 2250

       $\to z =\frac{2250- 1530}{316 } \\\\ \to z =\frac{720}{316 } \\\\ \to z = 2.27$

The z-score is = 2.27

If the value of z-score= 1420

       $\to z =\frac{1420- 1530}{316 } \\\\ \to z =\frac{-110}{316 } \\\\ \to z = -0.348$

The z-score is = -0.348