Question

pH measurements of a chemical solutions have mean 6.8 with standard deviation 0.02. Assuming all pH measurements of this solution have a nearly symmetric/bell-curve distribution. Find the percent (%) of pH measurements reading below 6.74 OR above 6.76.

Answer 1

Answer: 2.14 %

Step-by-step explanation:

Given : pH measurements of a chemical solutions have

Mean :  $\mu=6.8$

Standard deviation : $\sigma=0.02$

Let X be the pH reading of a randomly selected customer chemical solution.

We assume  pH measurements of this solution have a nearly symmetric/bell-curve distribution (i.e. normal distribution).

The z-score for the normal distribution is given by :-

$z=\dfrac{x-\mu}{\sigma}$

For x = 6.74

$z=\dfrac{6.74-6.8}{0.02}=-3$

For x = 6.76

$z=\dfrac{6.76-6.8}{0.02}=-2$

The p-value =$P(6.74<x<6,76)=P(-3<z<-2)$

$P(z<-2)-P(z<-3)=0.0227501- 0.0013499=0.0214002\approx0.0214$

In percent, $0.0214\times=2.14\%$

Hence, the percent of pH measurements reading below 6.74 OR above 6.76 = 2.14%