Question 749085: Grade point averages of math majors at a large distance education university are normally distributed with a mean of u= 2.85 and a standard deviation of σ=0.30. If a random sample of 25 math majors is selected from that university, what is the probability that the sample mean grade point averages will be
a) either less than 2.709 or more then 2.955?
b) at least 2.757?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Grade point averages of math majors at a large distance education university are normally distributed with a mean of u= 2.85 and a standard deviation of σ=0.30.
If a random sample of 25 math majors is selected from that university, what is the probability that the sample mean grade point averages will be
a) either less than 2.709 or more then 2.955?
t(2.709) = (2.709-2.85)/[0.3/sqrt(25)] = -2.35
P(x < 2.709) = P(t < -2.35) = tcdf(-100,-2.35,24) = 0.0137
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t(2.9557) = (2.9557-2.85)/[0.3/sqrt(25)] = 1.7617
P(x > 2.9557) = P(z > 1.7617) = tcdf(1.7617,100,24) = 0.0454
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Add those probabilities to get your answer.
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b) at least 2.757?
Use the same procedure.
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Cheers,
Stan H.
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