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devlian [24]
3 years ago
11

pH measurements of a chemical solutions have mean 6.8 with standard deviation 0.02. Assuming all pH measurements of this solutio

n have a nearly symmetric/bell-curve distribution. Find the percent (%) of pH measurements reading below 6.74 OR above 6.76.
Mathematics
1 answer:
aalyn [17]3 years ago
6 0

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

P(z

In percent, 0.0214\times=2.14\%

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

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