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Zorluk: KolayData Types, Distributions, and Descriptive Statistics

A public health physician is analyzing cholesterol levels in a suburban community. The total serum cholesterol levels of 1,0001,000 adult residents are recorded and found to follow a perfectly normal distribution. The mean total cholesterol level is 195195 mg/dL, and the standard deviation is 1515 mg/dL.

According to the empirical rule, what is the upper limit of the central range (in mg/dL) that symmetrically encompasses approximately 99.7%99.7\% of the residents' total cholesterol levels?

Cevap: 240 mg/dL

Cevap

240
For perfectly normally distributed data, the empirical rule (also known as the 68−95−99.768-95-99.7 rule) specifies that approximately 68%68\% of values lie within 11 standard deviation of the mean, 95%95\% within 22 standard deviations, and 99.7%99.7\% within 33 standard deviations. Since the population mean is 195195 mg/dL and the standard deviation is 1515 mg/dL, the upper limit encompassing the middle 99.7%99.7\% of the data is found by adding three standard deviations to the mean: 195+3(15)=195+45=240195 + 3(15) = 195 + 45 = 240 mg/dL.

Adım Adım Çözüm

1
Identify the mean and standard deviation from the vignette.
Mean = 195195 mg/dL, Standard Deviation (SD) = 1515 mg/dL.
These parameters mathematically define the normal distribution described in the study.
2
Determine the number of standard deviations needed for 99.7%99.7\% coverage.
33 standard deviations.
The empirical (68−95−99.768-95-99.7) rule states that 99.7%99.7\% of data in a normal distribution falls within 33 standard deviations of the mean.
3
Calculate the upper limit of this range.
195+3(15)=240195 + 3(15) = 240.
To find the upper bound symmetrically encompassing 99.7%99.7\% of the data, add exactly 33 standard deviations to the mean.

Anahtar Kavram

The empirical (68-95-99.7) rule for normal distributions
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Data Types, Distributions, and Descriptive Statistics

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