Question 975888: Suppose that a scholarship qualifying exam is given to a large number of students every year.
Over the last 5 years, the exam results are approximately normally distributed with a mean of 35 and a standard deviation of 7.
Suppose over that period of time 10000 students took the test
If you had received a 56, how many students (approximately) did better than you? What does that say about your score?
What if your friend received a 28? How many students (approximately) had a lower score than your friend?
If the scholarship is awarded to 2.5% of the students who take the exam, aproximatly what would be the minimum score that would be needed to qualify?
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! normal distribution with mean = 35, std dev = 7, 1000 students took exam
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P( X > 56) = 1 - P( X < 56 )
z-score = (56 - 35) / 7 = 3 and P( X < 56 ) = 0.9987
P( X > 56) = 1 - 0.9987 = 0.0013
now 1000 * 0.0013 = 1.3, since we can not have .3 person, there are 2 people did better than you. OR using rounding only 1 person did better than you
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P( X < 28 ), we calculate the z-score
z-score = (28 - 35) / 7 = -1
P( X < 28 ) = 0.1587
now 1000 * 0.1587 = 158.7, 159 students had a lower score than your friend
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2.5% = 0.0250
1 - 0.0250 = 0.9750
note 1.96 is the associated z-score for 0.9750
1.96 = (X - 35) / 7
X - 35 = (7 * 1.96)
X - 35 = 13.72
X = 48.72
X is approx 49
49 is the minimum score that would be needed to qualify
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