Question 1172801: Grade point averages of students on a large campus
follow a normal distribution with a mean of 2.6 and a
standard deviation of 0. 5.
a. One student is chosen at random from this cam-
pus. What is the probability that this student has a
grade point average higher than 3.0?
b. One student is chosen at random from this cam-
pus. What is the probability that this student has a
grade point average between 2.25 and 2.75?
c. What is the minimum grade point average needed
for a student's grade point average to be among
the highest 10% on this campus?
d. A random sample of 400 students is chosen from
this campus. What is the probability that at least 80
of these students have grade point averages higher
than 3.0?
e. Two students are chosen at random from this
campus. What is the probability that at least one of
them has a grade point average higher than 3.0?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! z=(x-mean)/sd
>(3.0-2.6)/0.5 or >0.8. Note; > or >= are the same since this is area from a given dimensionless point on the curve.
probability is 0.2119
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this is z between -0.7 and +0.3 is 0.3759. Also 2nd VARS2Normalcdf(2.25,2.75,2.6,0.5)ENTER
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the highest 10% is where z=1.282
1.282=(x-2.6)/0.5
0.641=x-2.6
x=3.241
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The probability of 1 being > 3.0 is 0.21185
for 80/400 or 0.2, do a 1 proportion z test
z>(0.2-0.21185)/sqrt(0.21185*0.78815/400)
z>-0.01185/0.0204=-0.5801
that probability is 0.7191 (calculator gives 0.7190)
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What is the probability that neither has that value? That is 0.7881^2 or 0.6211. So the answer is the complement of that value or 0.3789
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