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 3 decibels. What is the probability that a randomly selected jet will generate a noise level of more than 105 decibels?
A) 0.0228
B) 0.0475
C) 0.0485
D) 0.0500

Question

Quizplus · Accepted Answer

We need to find the probability that a randomly selected jet will generate a noise level of more than 105 decibels. Using the Z-score formula, we have:

Z = (X - μ) / σ
Z = (105 - 100) / 3
Z = 1.67

Using a standard normal distribution table or calculator, we find that the probability of Z being greater than 1.67 is 0.0475. Therefore, the probability that a randomly selected jet will generate a noise level of more than 105 decibels is 0.0475 or 4.75%. The best choice is B.

The Metropolitan Airport Commission Is Considering the Establishment of Limitations