Question

 

a) Treisa needs to score at the 95% percentile on an economics knowledge test to earn college credits forher job. All students tend to score 85 on average with a σx of 4.9. What z-score does she need to be atthe 95% percentile?

b) Treisa needs to score at the 95% percentile on an economics knowledge test to earn college credits forher job. All students tend to score 85 on average with a σx of 4.9. What raw score does she need to beat the 95% percentile?

c) As an instructor, I want to get a “normal” selection of current Psychology 10 students to speak to anew in-coming group on the importance of getting homework completed on time, coming to classregularly, and asking questions in class. Thus, I plan to select the most typical Psych 10 student in thecurrent semester to represent Psych 10 students. To do this, I will select those who score the middle 50% on a Psychology 10 exam. What range of raw scores do students have to achieve in order to beselected in this “typical” group of Psych 10 students when students in general tend to score 57 on thistest with a σx of 6.8 ?

Answer 1

a)

µ =    85                  
σ =    4.9                  
percentile=   0.95                  
                      
Z value at    0.95   =   1.645   (excel formula =NORMSINV(α))      
so,

z-score does she need to be atthe 95% percentile = 1.645

b)

z=(x-µ)/σ                      
so, X=zσ+µ=   1.645   *   4.9   +   85  
X   =   93.0598              

so, raw score = 93.06

c)

µ =    57                          
σ =    6.8                          
proportion= middle 50%

proportion left is equally distributed both sides

so, middle 50% is separated by 0.25 and 0.75.
                              
z value at   0.25   =   -0.674 (excel formula =NORMSINV(α))              
Z value at    0.75   =   0.674   
z=(x-µ)/σ                              
so, X=zσ+µ=                              
X1 =   -0.674 *   6.8   +   57   =   52.41  
X2 =   0.674 *   6.8   +   57   =   61.59

So, range of raw scores do students have to achieve in order to beselected in this “typical” group of Psych 10 students is (52.41,61.59)