Question

an instructor grades on a curve by assuming that grades on a test are normally distributed. If the average grade is 80 and the standard deviation is 8 find the test score for each grade interval if the instructor assigns grades

Answer 1

To find the test score for each grade interval, use z-scores and the standard normal distribution.

Step-by-step explanation:

To find the test score for each grade interval, we can use z-scores and the standard normal distribution. Since the average grade is 80 and the standard deviation is 8, we can calculate the z-score for each grade interval using the formula:

z = (x - µ) / σ

where z is the z-score, x is the test score, µ is the mean, and σ is the standard deviation. We can then use a z-table or calculator to find the corresponding area under the curve, which represents the probability of getting a grade within that interval. For example, if we want to find the test score for the interval corresponding to an A grade, which typically falls in the top 10% of scores, we can look up the z-score that corresponds to a top 10% area under the curve and solve for x.

Answer 2

Step-by-step explanation:

According to normal distribution curves following a bell curve formula, it is followed that

34% of people will lie between Mean point and one positive standard deviation

34% of people will lie between Mean point and one negative standard deviation

14% of people will lie between Mean point and two positive standard deviation

14% of people will lie between Mean point and two negative standard deviation

2% of people will lie between Mean point and three positive standard deviation

2% of people will lie between Mean point and three negative standard deviation

Now following this principle, we are given that mean score is 80 and standard deviation is 8, hence the interval for grades would be;

Grade A ; Score greater than 96

Grade B : Score greater than 88 and less than or equal to 96

Grade C : Score greater than 80 and less than or equal to 88

Grade D : Score greater than 72 and less than or equal to 80

Grade E : Score greater than 64 and less than or equal to 72

Grade F : Score less than 64