SOLUTION: 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

Question 1197054: 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 warnig for this car? (Round your answer to 2 decimal points.)
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 30 psi to 34 psi. Assume the tire's 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 recomended range? (Round your intermediate calculations and final answer to 4 decimal places.)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
a)At what psi will the TPMS trigger a warnig for this car? (Round your answer to 2 decimal points.)

target pressure = 32 psi.
28% below 32 = (1 - .28) * 32 = 23.04 psi.
when the target pressure gets below that, the tpms will warn the driver.

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.)

with a mean of 32 and a standard deviation of 3, the probability that the tpms will trigger a warning will be based on the following formula.
z = (x - m) / s
z is the z-score
x is the raw score
m is the mean
s is the standard deviation.
when x = 23.04 and m = 32 and s = 3, the formula becomes:
z = (23.04 - 32) / 3 = -2.9867 rounded to 4 decimal places.
probability of getting a z-score less than that is equal to .0014.

c)The manufacturer's recommended correct inflation range is 30 psi to 34 psi. Assume the tire's 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.)

z-score for psi of 30:
z = (30 - 32) / 3 = -.6667 rounded to 4 decimal places.
z-score for psi of 45:
z = (34 - 32) / 3 = .6667 rounded to 4 decimal places.
probability of getting a z-score less than -.6667 is equal to .2525 rounded to 4 decimal places.
probability of getting a z-score less than .6667 is equal to .7475 rounded to 4 decimal places.
probability of getting a z-score between -.6667 and .6667 is equal to .7475 minus .2524 = .4950.

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