Question

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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 N_i 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.

Answer 1