Answer to Question #4365 in Statistics and Probability for Chris
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:
-0.525 = (x-4.8)/1.45
x = 4.03875
Thus 30% of stays are less than 4.03875 days.
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Both variance and standard deviation are applied in statistics . Besides, you can see all calculations involve a standard deviation, not variance.
That damn variance got me. Forgot to turn it into a standard deviation!