Have you checked your blood sugar yet?

Probability Level 2

In annual check-up, a standard fasting blood sugar level has a normal range of 75 to 115 mg/dL, claimed to cover approximately 95% of the world's population.

What is the cut-point integer value of high sugar level $\big($ beyond $99^\text{th}$ percentile $\big)$ in an individual? (You don't have to be a doctor to diagnose diabetes.)

The answer is 125.

1 solution

Worranat Pakornrat
Dec 24, 2016

Relevant wiki: Standard Deviation

In a normal distribution, the data can be pooled with the use of the standard deviation , in this case $95$ % of the population's data range from $75$ to $115$ , which is $\pm 2\sigma$ from the mean $\mu$ .

In other words, $115 = \mu + 2\sigma$ , and $75 = \mu - 2\sigma$ .

Therefore, $\mu = 95$ and $\sigma = 10$ .

To cover $99.7$ % of the world's population, the data will range from $\mu - 3\sigma$ to $\mu + 3\sigma$ or from $65$ to $125$ .

Therefore, any value greater than $\boxed{125}$ is considered diabetes.

But is it not beyond 99th percentile that is needed ? Why cover 99.7% of the population ?

Gabin Kolly - 3 years, 2 months ago

Have you checked your blood sugar yet?

The answer is 125.

1 solution

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