t the present time, the noise level per jet takeoff in one neighborhood near the airport is ormally distributed with a mean of 100 decibels and a standard deviation of 6 decibels. ion of jets generates a noise level greater than 105 decibels at takeoff in this neighborh are selected at random, what is the probability that at least 2 will generate noise in exc at least 2 will not generate noise in excess of 105 decibels? gulation is passed that requires jet noise in this neighborhood to be lower than 105 deci Assuming the standard deviation of the noise distribution remains the same, how much noise have to be lowered to comply with the regulation?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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The metropolitan airport commission is considering the establishment of limitations on noise pollution around
a local airport. At the present time, the noise level per jet takeoff in one neighborhood near the airport is
approximately Normally distributed with a mean of 100 decibels and a standard deviation of 6 decibels.
(a) What proportion of jets generates a noise level greater than 105 decibels at takeoff in this neighborhood?
(b) If six takeoffs are selected at random, what is the probability that at least 2 will generate noise in excess of
105 decibels and at least 2 will not generate noise in excess of 105 decibels?
(c) Suppose a regulation is passed that requires jet noise in this neighborhood to be lower than 105 decibels
90% of the time. Assuming the standard deviation of the noise distribution remains the same, how much will
the mean level of noise have to be lowered to comply with the regulation?
Transcribed Image Text:The metropolitan airport commission is considering the establishment of limitations on noise pollution around a local airport. At the present time, the noise level per jet takeoff in one neighborhood near the airport is approximately Normally distributed with a mean of 100 decibels and a standard deviation of 6 decibels. (a) What proportion of jets generates a noise level greater than 105 decibels at takeoff in this neighborhood? (b) If six takeoffs are selected at random, what is the probability that at least 2 will generate noise in excess of 105 decibels and at least 2 will not generate noise in excess of 105 decibels? (c) Suppose a regulation is passed that requires jet noise in this neighborhood to be lower than 105 decibels 90% of the time. Assuming the standard deviation of the noise distribution remains the same, how much will the mean level of noise have to be lowered to comply with the regulation?
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