Question

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 measurement of a randomly selected water specimen is a value between 7.5 and 8.2?

A. 0.3003
B. 0.6997
C. 0.9522
D. 0.9902

Answer 1

0.699733

Explanation:

Given that :

Mean (m) = 8

Standard deviation (s) = 0.3

Probability that pH is between 7. 5 and 8.2

Probability of pH < 7.5

P(x < 7.5)

The standardized score (Z) :

Z = (x - m) / s

Z = (7.5 - 8) / 0.3 = - 1.6667

p(Z < - 1.6667) = 0.047787 ( Z probability calculator)

Probability of pH < 8.2

P(x < 8.2)

The standardized score (Z) :

Z = (x - m) / s

Z = (8.2 - 8) / 0.3 = 0.6667

p(Z < 0.6667) = 0.74752 ( Z probability calculator)

Hence,

p(Z < 0.6667) - p(Z < - 1.6667)

0.74752 - 0.047787 = 0.699733