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.)

(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.)

(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 andfinal answer to 4 decimal places.)