Question

If Michael has a z-score of -2 on his statistics quiz, what proportion of his classmates scored higher on the quiz

a) 0.50
b) 0.84
c) 0.98
d) 0.68

If the upper 30% of a normally distributed class passed a quiz, what was the lowest score a student could have received & still have passed if the class average was 70 with standard deviation of 10

a) 75.2
b) 70.0
c) 64.8
d) 60.2

If you are going to predict future performance on the basis of a sample mean and sample standard deviation it is desirable to have

a) A small mean
b) A small standard deviation
c) A large mean
d) A large standard deviation

Answer 1

1)

Z score= -2

P(Z > -2) = 0.98

excel formula for probability from z score is =NORMSDIST(Z)

If Michael has a z-score of -2 on his statistics quiz, 0.98 proportion of his classmates scored higher on the quiz

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µ=   70                  
σ =    10                  
upper 30% =bottom 70% or proportion=   0.70   
                      
Z value at    0.7   =   0.5244   (excel formula =NORMSINV(   0.70   ) )
z=(x-µ)/σ                      
so, X=zσ+µ=   0.524   *   10   +   70  
X   =   75.2

answer: 75.2

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