SOLUTION: A group of more than 1000 students took a test in Mathematics and their final grades have a mean of 70 and a standard deviation of 10. If we can approximate the distribution of the
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Question 1149161: A group of more than 1000 students took a test in Mathematics and their final grades have a mean of 70 and a standard deviation of 10. If we can approximate the distribution of these grades by a normal distribution, what percent of the students
(a) scored higher than 80?
(b) should pass the test (grades ≥ 60)? Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! (a) Probability (P) (X > 80) = 1 - P(X < 80)
:
z-score(80) = (80 - 70)/10 = 1
:
Lookup a z-score of 1 in the table of z-values and its associated P
:
P(X < 80) = 0.8413
:
P(X > 80) = 1 - 0.8413 = 0.1587
:
(b) z-score(60) = (60 -70)/10 = -1
:
P(X < 60) = 0.1587
:
P(X > 60) = 1 - 0.1587 = 0.8413
:
