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. a). What is, approximately, the probability that the pH measurement of a randomly selected water specimen is greater than 8.2?
b). What is, approximately, the probability that the pH measurement of a randomly selected water specimen is a value between 7.5 and 8.2?
c) Find the first quartile of the distribution of the pH measurements. i. e., Find the pH value such that three-quarters of the pH measurements in this river basin are greater than this value.

a

b

c

Step-by-step explanation:

From the question we are told that

   The  mean is  

   The standard deviation is  

probability that the pH measurement of a randomly selected water specimen is greater than 8.2 is mathematically evaluated as

From the z table  the area under the normal curve to the left corresponding to  0.667  is

So

Generally the probability that the  that the pH measurement of a randomly selected water specimen is a value between 7.5 and 8.2 is mathematically represented as

=>    

=>    

From the z table the area under the normal curve to the left corresponding to  -2.667 and  0.667   is

and  

So  

=>

Generally 25% of the pH measurements is below the first quartile of the distribution

  Hence the probability of the obtaining a value below the  first quartile is mathematically represented as

=>  

Generally from the normal distribution table the critical value corresponding to 0.25  is  

So

=>