Question

The voltage in a certain circuit is a normal random variable with mean 120 and standard...

The voltage in a certain circuit is a normal random variable with mean 120 and standard deviation 5. Sensitive equipment will be damaged if the voltage is not between 112 and 128. What is the probability that the equipment will be damaged?

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Answer #1

Solution:

Given that,

mean =  = 120

standard deviation =  = 5

p ( 112 < x < 128 )

= p (112 - 120 / 5) < ( x -  / ) < ( 128-120/5)

= p ( - 8 / 5 < z < 8 / 5 )

= p (- 1.6<z <1.6 )

= p (z < 1.6 ) - p ( z < - 1.6 )

Using z table

= 0.9452 - 0.0548

= 0.8904

Probability = 0.8904

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