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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

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 32 psi (pounds per square inch.)

(a) At what psi will the TPMS trigger a warning for this car?

(b) Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 3 psi. 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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