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. ​(a) What is the maximum score that can be in the bottom 20​% of​ scores? ​(b) Between what two values does the middle 60​% of scores​ lie? mean=3.3 SD=0.81

Answer 1

solution

Using standard normal table,

P(Z < z) =20 %

= P(Z < z) = 0.20  

= P(Z < - 0.84) = 0.20

z =- 0.84 Using standard normal table,

Using z-score formula  

x= z * +

x=- 0.84 *0.81+3.3

x= 2.6196

(B)

middle 60% of score is

P(-z < Z < z) = 0.60

P(Z < z) - P(Z < -z) = 0.60

2 P(Z < z) - 1 = 0.60

2 P(Z < z) = 1 + 0.60 = 1.60

P(Z < z) = 1.60 / 2 = 0.8

P(Z <0.84 ) = 0.8

z  ± 0.84 using z table

Using z-score formula  

x= z * +

x= -0.84 *0.81+3.3

x= 2.6191

z = 0.84

Using z-score formula  

x= z * +

x= 0.84 *0.81+3.3

x= 3.9804

answer=2.6191 to 3.9804