Question

The test scores for the analytical writing section of a particular standardized test can be approximated by a normal​ distribution, as shown in the figure. Mean = 3.3 and standard deviation = 0.93

​(a) What is the maximum score that can be in the bottom 5​% of​ scores?

​(b) Between what two values does the middle 90​% of scores​ lie?

Answer 1

a) For bottom 5% z value = -1.645

So, 1.77 is the maximum score that can be in the middle 5% of scores.

b) For middle 90% values we need to remove bottom 5% and top 5%

For bottom 5% z values = -1.645

For top 5% z-values = 1.645

So, middle 90% scores lies between 1.77 to 4.83.

Please comment if any doubt. Thank you.