In: Statistics and Probability
The Metropolitan Aviation Commission is considering setting limits on noise pollution around a local airport. Currently, the noise level produced by a plane taking off, measured from one of the neighborhoods near the airport, follows a normal distribution with an average of 99 decibels and a standard deviation of 5 decibels.
a) What is the probability that the generated noise level is at least 99 decibels? exactly 99 decibels?
b) Suppose there is a regulation that the noise level remains below 104 decibels in that area, what proportion of the takeoffs will be violating the regulation?
c) If the airport administration wants to be able to comply with the regulation at least 95% of the time (only 5% of takeoffs violate the regulation), to what level is it necessary to reduce the average noise level?
d) If 34 of these planes take off during the week, what is the probability that at least 9 of them violate the regulation?