Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 25% 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 2 psi. If the car’s average tire pressure is on target, what is the probability that the TPMS will trigger a warning? (c) The manufacturer’s recommended correct inflation range is 30 psi to 34 psi. Assume the tires’ average psi is on target. If a tire on the car is inspected at random, what is the probability that the tire’s inflation is within the recommended range?

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