Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pres Suppose the target tire pressure of a certain car is 30 psi (pounds per square inch.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% 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 places.*)
When the tire pressure is [Click to select] psi.
(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? (*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 _____](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F894b117a-73d1-4c54-bfe4-4be20ac5dc63%2F31a300e6-2d21-4814-beaa-b743fbf893f9%2F0tctks.jpeg&w=3840&q=75)
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