Question 1182505: College Costs The mean undergraduate cost for
tuition, fees, room, and board for four-year institutions
was $26,489 for a recent academic year. Suppose
that s $3204 and that 36 four-year institutions are
randomly selected. Find the probability that the sample
mean cost for these 36 schools is
a. Less than $25,000
b. Greater than $26,000
c. Between $24,000 and $26,000
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Fewer than $25,000:
z=(x bar-mean)/sigma/sqrt(n)
=(25000-26489)/3204/6
=-1489*6/3204
=-2.78
since we want less than that, the probability is 0.0026, rounding the z at the end
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Greater than $26,000:here z=(-489)*6/3204 or -0.9157 for probability of 0.8201
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fewer than $24,000 has virtually no probability, so this is less than $26,000, which is the complement of the last answer or 0.1799.
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Check the last by 2nd VARS normalcdf(24,000,26000,26489,3204/6), since the true sd of this mean distribution is 3204/sqrt(36).
=0.1799
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