Problema Solution
Final averages are typically approximately normally distributed with a mean of 73 and a standard deviation of 9.5. Your professor says that the top 9% of the class will receive an A; the next 15%, a B; the next 40%, a C; the next 23%, a D; and the bottom 13%, an F. (Give your answers correct to one decimal place.)
(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.)
Answer provided by our tutors
a) P(X>x) = 0.09
P[Z > (x- 73) / 9.5] = 0.09
P[Z > (x- 73) / 9.5] = P(Z > 1.34)
on comparing
(x -73) /9.5 = 1.34
x= 85.73
He should score more than 85.7to get an A
b)
P(X>x) = 0.09+0.15+0.40
P[Z > (x- 73) / 9.5] = 0.64
P[Z > (x- 73) / 9.5] = P(Z > -0.35846)
on comparing
(x -73) /9.5 = -0.35846
x= 69.6
He should score more than 69.6 to get a C or better
c) P(X>x) = 0.09+0.15+0.40+0.23
P[Z > (x- 73) / 9.5] = 0.87
P[Z > (x- 73) / 9.5] = P(Z > -1.12)
on comparing
(x -73) /9.5 = -1.12
x= 62.3
He should score more than 62.3 to Pass