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 
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Note: Most texts require use of the t-distribution on problems involving
the sample mean.
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t(375) = (375-406)/[98/sqrt(45)] = -2.1220
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t(450) = (450-406)/[98/sqrt(45)] = 3.0118
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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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