Question

The pH measurements of water specimens from various locations along a given river basin are normally distributed with mean 8 and standard deviation 1.3. 2.

What is the probability that the pH measurement of a randomly selected water specimen is a value between 7.5 and 8.2?

Answer 1

u= 8,0 = 1.3

the probability that the pH measurement of a randomly selected water specimen is a value between 7.5 and 8.2 is :-

= P(7.5 < X < 8.2

X-8 7.5 – 8 = P( 1.3 8.2 - 8 1.3 1.3

P(-0.3846 < 3 < 0.1538)

- P(Z < 0.1538) - P(Z < -0.3846

Φ(0.1538) Φ -0.3846)

Φ(0.1538) - (1 – Φ(0.3846))

Φ(0.1538) – 1+ Φ(0.3846)

[ in any blank cell of excel type =NORMSDIST(0.1538) ]

=0.5611-1+0.6497

[ in any blank cell of excel type =NORMSDIST(0.3846) ]

= 0.2108

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