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25 December, 04:44

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?

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Answers (1)
  1. 25 December, 04:59
    0
    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
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