statistics question?

Question

how do you determine this so I can learn how to do it myself

Which one is the lowest grade?

1st test, score of 79,with a mean of 67,standard deviation of 4
2nd test,score of 65 ,with a mean of 70,standard deviation of 15
3rd test score of 51 with a mean of 75,standard deviation of 3

Answer 1

we can standardized the score so that they are in same measure of units (in terms of standard deviation from the mean) and comparable

formula: standard score= (x - mean)/standard deviation

1st test
z1 = (79-67)/4 = 3
z2 = (65-70)/15 = -5/15 = -0.33
z3= (51-75)/3 = -8

lowest grade is in 3rd test

Answer 2

how you would grade would be this

if you have 100 questions and get 15 wrong you would do this
100-15=(85)
(85)X100=8500
8500/100=85
the answer would be 85%

I hope this help get you to your answer