Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 28% below the target pressure. Suppose the

Question

Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 28% below the target pressure. Suppose the target tire pressure of a certain car is 30 psi (pounds per square inch.)
(a) At what psi will the TPMS trigger a warning for this car?
(b) Suppose the tire pressure is a normally distributed random variable with a standard deviation equal to 2psi. If the car’s average tire pressure is on target, what is the probability that the TPMS will trigger a warning?

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Cora 3 weeks 2021-10-01T04:27:55+00:00 1 Answer 0

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    2021-10-01T04:29:36+00:00

    Answer:

    2.95\times10^{-5}

    Step-by-step explanation:

    a)The pressure level that will trigger a warning is

    30 – 30*0.28 = 21.6 psi

    b) The probability that the TPMS will trigger warning at 21.6 psi, given that tire pressure has a normal distribution with average of 30 psi and standard deviation of 2 psi is:

    f(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}

    where x = 21.6, μ = 30 and σ = 2

    f(22.94)={\frac {1}{2 {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {21.6-30}{2 }}\right)^{2}}

    f(22.94)=0.2e^{-8.82} = 2.95\times10^{-5}

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