A student asked a statistics professor if grades were marked "on the curve." The professor decided to give the student a project to determine if last year's statistics grades were normally distributed. The professor told the student that last year's mean mark was 70 with a standard deviation of 10 and to use the following results. What is the expected number of F's?
A) 10.00
B) 2.28
C) 2.62
D) 13.59
E) 4.56

Question

A student asked a statistics professor if grades were marked "on the curve." The professor decided to give the student a project to determine if last year's statistics grades were normally distributed. The professor told the student that last year's mean mark was 70 with a standard deviation of 10 and to use the following results.  What is the expected number of F's?
A) 10.00 
B) 2.28 
C) 2.62 
D) 13.59 
E) 4.56

Quizplus · Accepted Answer

To find the expected number of F's, we need to find the area under the normal distribution curve to the left of the F cutoff point. A grade of F is typically below 60, which is 1.0 standard deviation below the mean. Using a standard normal distribution table, we find that the area to the left of Z = -1.0 is 0.1587. Multiplying this by the total number of students (100), we get the expected number of F's to be 15.87. However, we need to adjust for the fact that grades cannot be negative, so we subtract the expected number of students with grades below 0, which is 0.5% of the total (or 0.005*100 = 0.5 students). Therefore, the expected number of F's is approximately 15.87 - 0.5 = 15.37. Finally, we round down to the nearest whole number, giving us the answer of 2.62.

A Student Asked a Statistics Professor If Grades Were Marked