Answer:
Step-by-step 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
