Final averages are typically approximately normally distributed with a mean of 66 and a standard deviation of 10.5. Your professor says that the top 5% of the class will receive an A; the next 15%, a B; the next 47%, a C; the next 22%, a D; and the bottom 11%, an F.

Question

Final averages are typically approximately normally distributed with a mean of 66 and a standard deviation of 10.5. Your professor says that the top 5% of the class will receive an A; the next 15%, a B; the next 47%, a C; the next 22%, a D; and the bottom 11%, an F.
(a) What average must you exceed to obtain an A?

(b) What average must you exceed to receive a grade of C or better?

(c) What average must you obtain to pass the course? (You'll need a D or better.)

Reiny · Answer

I will let you play with

http://davidmlane.com/normal.html

click on "value from an area" and enter
mean: 66
sd: 10.5
click on below and enter .95 in area
I get 83.275
So 95% of the students will have a score of less than 83

the next 15 % will get a B
so 20 % will get either A or B
and 80% will not get A or B

click on below and enter .8 in area
I got 74.835 or 75% to 83 will get you a B
67% will get at least a C
enter .67 in area to get 70.615

I will let you continue