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Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is...

Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 27% 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? (Round your answer to 2 decimal place.)

When the tire pressure is           (Click to select)  above  below   psi.

(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? (Round your answer to 4 decimal places.)

Probability           

(c) The manufacturer’s recommended correct inflation range is 28 psi to 32 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? (Round your intermediate calculations and final answer to 4 decimal places.)

Probability           

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