Question 754102: 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
Stanbon answered:
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
I don't under how 0.0137 was calculated. Why isn't the solution this:
z=-2.35 (calculated above) so P (z<-2.35)=0.0094 <
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
Stanbon answered:
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
I don't under how 0.0137 was calculated. Why isn't the solution this:
z=-2.35 (calculated above) so P (z<-2.35)=0.0094 <
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You are correct if you use a z-distribution. If that is what
your text calls for, use it.
Many texts call for use of the t-distribution when dealing
with sample means.
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Cheers,
Stan H.
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