SOLUTION: The New England Journal of Medicine reported that the population mean and standard deviation figures for the cost per case for patients with medical back problems are $406 and $98,

Question 789482: The New England Journal of Medicine reported that the population mean and standard deviation figures for the cost per case for patients with medical back problems are $406 and $98, respectively. What's the probability that the mean cost per case for a random sample for 45 patients with medical back problems is between $375 and $450?
Mean = 406
SD= 98
sample size (n)= 45
I know how to find z-scores and SD of similar questions but I don't know how to solve equations that ask to estimate new means. I don't know if that makes sense, but in any case, I have no idea how to solve the above equation. Any help is very much appreciated. Thanks!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The New England Journal of Medicine reported that the population mean and standard deviation figures for the cost per case for patients with medical back problems are $406 and $98, respectively. What's the probability that the mean cost per case for a random sample for 45 patients with medical back problems is between $375 and $450?
Mean = 406
SD= 98
sample size (n)= 45
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Note: Most texts require use of the t-distribution on problems involving
the sample mean.
---------------
t(375) = (375-406)/[98/sqrt(45)] = -2.1220
-----
t(450) = (450-406)/[98/sqrt(45)] = 3.0118
------
P(375< x-bar < 450) = P(-2.1220 < t < 3.0118)
= tcdf(-2.1220,3.0118,44) = 0.9781
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Cheers,
Stan H.
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