Answer to Question #4365 in Statistics and Probability for Chris
The average length of a hospital stay for all diagnoses is 4.8 days. If we assume that the lengths of hospital stays are normally distributed with a variance of 2.1, then 10% of hospital stays are longer than how many days? Thirty percent of stays are less than how many days?
First let's calculate the standard deviation. Variance = (standard deviation)^2 Standard deviation = sqrt(2.1) Standard Deviation = 1.45 Now we must use z-scores. To find the top 10% of hospitals, we must find the z-score that corresponds to 90%. Looking at a z-score table, we look for 0.9000 and can find this z-score to be about 1.28. Then with the formula for z-scores, we can find the corresponding value.
z = (x-μ)/σ 1.28 = (x-4.8)/1.45 x = 6.656
Thus 10% of hospital stays are longer than 6.656 days. To find the lowest 30% we can look for 0.3000 and can find this z-score to be about -0.525. Then again with the z-score formula we have:
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