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You are in charge of monitoring the pressure of a compressed air tank in a processing plant. After repeating the pressure measurement a large number of times, you found that the pressure values have Gaussian distribution with a mean value of 69 psi and a standard deviation of 10 psi. If it is important that the pressure stays below 84 psi, what is the probability (in percent) that the pressure will exceed this value

Respuesta :

Answer:

11.5

Step-by-step explanation:

Given that :

I am in charge of the pressure reading in a compressed air tank of a processing plant.

The Gaussian distribution having a mean value = 69 psi

Standard deviation = 10 psi

Here we have to find the probability that the pressure will exceed 84 psi.

So,

[tex]P(X \geq 84) = P \left(\frac{X - 69}{10} > \frac{84-69}{10} \right)[/tex]

                  [tex]$=P(Z > 1.5)$[/tex]

                  [tex]$=1-P(Z < 1.5)$[/tex]

                   = 0.115

                   = 11.5