Question

A noise level of a lawn tractor is approximately

normallydistributed with a mean of 100 decibels and a
standarddeviation of 3 decibels. What is the probability that a
arandomly slected lawn tractor will generate a noise level of
morethan 105 decibels?

Answer 1

Explanation:

Since the noise level of a lawn tractor is approximately

normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - u)/s

Where

x = the noise level

u = mean noise level

s = standard deviation

From the information given,

u = 100 decibels

s = 3 decibels.

We want to find the probability that a randomly selected lawn tractor will generate a noise level of

more than 105 decibels. It is expressed as

P(x > 105) = 1 - P(x ≤ 105)

For x = 105,

z = (105 - 100)/3 = 1.67

Looking at the normal distribution table, the probability corresponding to the z score is 0.9525

P(x > 105) = 1 - 0.9525 = 0.0475