Normal distribution mean and a standard deviation?

Question

Final examination grades in an introductory stat course is normally distributed with a mean of 73 and a standard deviation of 8


If the professor grades on a curve (gives A's to the top 10% of the class regardless of the score) are you better off with a grade of 81 on this exam or a grade of 68 on a different exam where the mean is 62 and the standard deviation is 3? Answer statistically and explain

Answer 1

Break out your friendly z-score tables or diagram and consider where you would be in the two competing distributions. In the first, you are at mean+1 sd and in the second, you are at mean+2 sd. I think you can take it from there.

Answer 2

P[X > 3200] = 0.06 P[Z > (3200-m)/s] = 0.06 (3200-m)/s = a million.555 3200 - m = a million.555s ---- equation a million additionally, P[X < 2600] = 0.14 P[Z < (2600-m)/s] = 0.14 (2600-m)/s = -a million.09 2600 - m = -a million.09s --- equation 2 remedy equations a million&2 for m and s.