# Probability of Hypokalemia w/ 1 or Multiple Measurements

• SakuRERE
In summary, the conversation discusses the probability of a patient being diagnosed with hypokalemia based on one measurement and multiple measurements taken on separate days. The first part of the question is solved using a standardized normal distribution and the second part is still uncertain. There is a formula used to calculate the probability of getting more positives than negatives, but it is unclear if this is the correct approach. Further information is needed in the problem statement to fully understand and accurately solve the question.f

#### SakuRERE

Misplaced Homework Thread moved from the technical forums
TL;DR Summary: Finding the probability with one measurement and multiple measurements on separate days.

Question: Hypokalemia is diagnosed when blood potassium levels are low, below 3.5 mmol/L. Let’s assume we know a patient whose measured potassium levels vary daily according to N(µ = 3.8 mmol/L, σ = 0.2 mmol/L).
(a) If a single potassium measurement is made, what is the probability that the patient is diagnosed as hypokalemic?
(b) If measurements are made instead on 4 separate days, what is the probability that the patient is diagnosed with hypokalemia?

For part A -->

I solved the question as a standardized normal distribution. I tried to find P(x<=3.5),
using the standard normal formula z= X-Mean/SD I converted the X value 3.5 to a Z score and got P(x<=-1.5)
after that, I used the Gauss table to find the probability and it was P(x<=-1.5)= 0.0668
this answer was similar to the answer key provided by our professor.

However, for the second part, the answer key has to be 0.0013 but I can't think of a way to figure it out. And I don't understand how taking different measurements on separate days will influence my probability.
I will appreciate your help, thank you!

I attached the positive and negative Gauss tables for easier accessibility.

#### Attachments

What does it even mean to be diagnosed after 4 samples? Do you have to get at least one positive? All positive?

The odds of getting more positives than negatives are
##4(.0668)^3(1-.0668)+.0668^4\approx 0.00113## which is not that far from what the answer key says...

• FactChecker
Or an average of the four below 3.5?

What does it even mean to be diagnosed after 4 samples? Do you have to get at least one positive? All positive?

The odds of getting more positives than negatives are
##4(.0668)^3(1-.0668)+.0668^4\approx 0.00113## which is not that far from what the answer key says...
But I didn’t get what’s that formula you used

Thanks again