SOLUTION: What propotion of A students studying statistics ? The amount of time devoted to studying statistics each week by students who achieve a grade of A in the course is a normally dis

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Question 1090265: What propotion of A students studying statistics ?
The amount of time devoted to studying statistics each week by students who achieve a grade of A in the course is a normally distributed random variable with a mean of 7.5 hours and a standard deviation of 2.1 hours.
a) What propotion of A students study for more than 10 hours per week.?
b) Find the probability that an A student spends between 7 and 9 hours studying?
c) What propotion of A students spend less than 3 hours studying?
d) What is the amount of time below which only 5% of all A students spend studying?
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Answer by rothauserc(4718) About Me  (Show Source):
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a) z-score = (10 - 7.5) / 2.1 = 1.19
Probability (P) ( X < 10 ) = 0.8830 approximately 0.88
P ( X > 10 ) = 1 - 0.88 = 0.12
proportion of A students study > 10 hours per week = 12/100 = 3/25
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b) z-score = (9 - 7.5) / 2.1 = 0.7143
P ( X < 9 ) = 0.7611
z-score = (7 - 7.5) / 2.1 = -0.2381
P ( X < 7 ) = 0.4052
P ( 7 < X < 9 ) = 0.7611 - 0.4052 = 0.3559
:
c) z-score = (3 - 7.5) / 2.1 = −2.1429
P ( X < 3 ) = 0.0162 approximately 0.02
proportion of A students who study < 3 hours per week = 2/100 = 1/50
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d) z-score associated with 5% is -1.65
-1.65 = (X - 7.5) / 2.1
X - 7.5 = -1.65 * 2.1 = −3.465
X = 7.5 -3.465 = 4.035 approximately 4
only 5% of all A students spend studying less than 4 hours
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