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 approximately, the probability that the ph measurements of a randomly selected water specimen is value between 7.5 and 8.2

The probability is 0.7011.

Z-scores are computed using the formula

z = (X - μ)/σ

The z-score for the lower limit is
z = (7.5 - 8)/0.3 = -1.67

The z-score for the upper limit is
z = (8.2 - 8)/0.3 = 0.67

Using a z-table (http://www.z-table.com) we see that the area to the left of the lower limit, less than that, is 0.0475.  The area to the left of the upper limit, less than that, is 0.7486.  To find the area between them we subtract:

0.7486 - 0.0475 = 0.7011

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