Question

An airport is studying the noise levels of jets during takeoff as they pass over a neighborhood. They find that at the present time, the mean noise level is 103 decibels and the standard deviation is 5.4 decibels. The distribution of noise levels for all jets during takeoff over the neighborhood has a normal distribution. What percent of these jets have a noise level less than 92.2 decibels when taking off over this neighborhood

Answer 1

Answer: 2.28%

Explanation:

Given: An airport find that at the present time, the mean noise level is 103 decibels and the standard deviation is 5.4 decibels.

The distribution of noise levels(x) for all jets during takeoff over the neighborhood has a normal distribution.

The probability that jets have a noise level less than 92.2 decibels when taking off over this neighborhood will be :-

`P(X<92.2)=P((X-\mu)/(\sigma)}<(92.2-103)/(5.4))\\\\=P(Z<-2)\\\\=1-P(Z<2)\\\\=1- 0.9772498\ \ \ [\text{By p-value table}]\\\\=0.0227502\approx2.28\%`

Hence, the percent of these jets have a noise level less than 92.2 decibels when taking off over this neighborhood = 2.28%