Question

Your friend usually gets a 76% on their tests and you get an 80%. If final test is worth 300 points, how often will your friend randomly get more points than you on the test ?

Thats what I was asked to solve, no more info given. Please if you can do it, I have to submit it today

Answer 1

Here

Your friend =A

Mean = np =    300   *   0.760   =           228.000
Variance = np(1-p) =    300   *   0.760   * ( 1 -    0.760   ) =   54.7200

Your = B

Mean = np =    300   *   0.800   =           240.000
Variance = np(1-p) =    300   *   0.800   * ( 1 -    0.800   ) =   48.0000

P(A-B >0)

Mean = 228 - 240 = -12
Variance = 54.72+ 48.0000 = 102.72

µ =    -12                  
σ = sqrt(102.72) = 10.13508757                  
                      
P ( X ≥   0.00   ) = P( (X-µ)/σ ≥ (0--12) / 10.1350875674559)              
= P(Z ≥   1.184   ) = P( Z <   -1.184   ) =    0.1182   (answer)

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