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Probability of attaining different grades in a statistics class.

In a large section of statistics class, the points for the final exams are normally distributed with a mean of 72 and a standard deviation of 9. Grades are to be assigned according to the following rule.

1) the top 10% receive A
2) the next 20% receive B
3) the middle 40%receive C
4) the next 20% receive D
5) the bottom 10% receive F.

Find the lowest score on the final exam that would qualify a student for an (A, B, C, D)

Solution Preview

1)
P[Z>Z0 ] = .1
P[0<z<z0] = .4 =
Z0 = 1.28
X = 1.28*9+72 = 83.52

2)
P[ X0< X < 83.62] =
P [ Z0 < Z < 1.28 ] = 0.2

0.3997 - ...

$2.19