Frank and Chris both took the ABC achievement test, which is N(950,50). If frank had a z-score of 2.5 and Chris had a score of 675, how much higher was Frank's score?
1075
1700
400
525
none of the above

Explanation:

The notation N(950,50) tells us that we have a normal distribution with the following parameters:

Use the z score z = 2.5 to convert to its raw score x

z = (x-mu)/sigma

2.5 = (x-950)/50

2.5*50 = x-950

125 = x-950

x-950 = 125

x = 125+950

x = 1075

Frank's z score of z = 2.5 corresponds to the actual score of x = 1075. This is 1075-675 = 400 points higher than the score Chris got.

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