The pH measurements of water specimens from various locations along a given river basin are Normally distributed with mean 8 and standard deviation 0.3.
What is the approximate probability that the pH measurement of a randomly selected water specimen is a value between 7.5 and 8.2?

Question

Quizplus · Accepted Answer

Use the Z-score formula:

Z = (X - μ) / σ

where X is the pH measurement, μ is the mean (8), and σ is the standard deviation (0.3).

For the lower bound of 7.5:

Z = (7.5 - 8) / 0.3 = -1.67

For the upper bound of 8.2:

Z = (8.2 - 8) / 0.3 = 0.67

Using a standard Normal distribution table or calculator, we can find the area between these two Z scores:

P(-1.67 ≤ Z ≤ 0.67) = 0.6997

Therefore, the approximate probability that the pH measurement of a randomly selected water specimen is a value between 7.5 and 8.2 is 0.6997.

The PH Measurements of Water Specimens from Various Locations Along