A set of final examination grades in an introductory quantitative analysis course is normally distributed, with a mean of 73 and a standard deviation of 8.
a) What is the probability of getting a grade below 91 on this exam?
b) What is the probability that a student scored between 65 and 89?
c) The probability is 5% that a student taking the test scores higher than what grade?
If the professor grades on a curve (that is, 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? Please explain your answer statistically only.
Step by step solution to the problem is provided.