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SHOW ALL WORK The power level of noise in the warehouse is measured in Watts and...

SHOW ALL WORK

The power level of noise in the warehouse is measured in Watts and is normally distributed with a mean of 1 Watt and a variance of 3 Watts. Government regulations require employees to wear noise cancelling headphones if the metric

X = (N1+N2+N3)/4

is greater than 2.5 Watts, where Ni for i=1,2,3 are independent measurements of the noise power level taken at three random times during the day.

a) Calculate the probability that the first noise N1 is greater that 2 Watts.

b) Calculate the probability that noise cancelling headphones will become necessary.

Math   Statistics-And-Probability   
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