Question

9) The national average SAT score (for Verbal and Math) is 1028. The distribution of the SAT score is a normal with. If the top 1% of the students will receive a $400 scholarship, what is the minimum score a student would need to score to receive the reward? 10) The average charitable contribution itemized per income tax return in Pennsylvania is $792. Suppose that the distribution of contributions is normal with a standard deviation of $103. Find the limits for the middle 60% of contributions.

data inefficiency??

Answer 1

10)

µ =    792                      
σ =    103                      
proportion=   0.6000                      
proportion left    0.4000   is equally distributed both left and right side of normal curve                   
z value at   0.2   = ±   0.842   (excel formula =NORMSINV(   0.40   / 2 ) )  
                          
z = ( x - µ ) / σ                          
so, X = z σ + µ =                          
X1 =   -0.842   *   103   +   792   =   705.313
X2 =   0.842   *   103   +   792   =   878.687

limits are (705.31 , 878.69)

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for ques 9), std dev is not given