### Tire Pressure Monitoring Systems (TPMS) Alert Parameters#### Problem ContextTire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 24% below the target pressure. Suppose the target tire pressure of a certain car is 29 psi (pounds per square inch).#### Questions**(a) At what psi will the TPMS trigger a warning for this car? (Round your answer to 2 decimal places.)****Answer:**- When the tire pressure is below [\[Input Box\]] psi.**Explanation:**- To find the trigger pressure, calculate 24% of the target pressure (29 psi) and subtract the result from the target pressure: \[ \text{Trigger Pressure} = 29 - (0.24 \times 29) = 29 - 6.96 = 22.04 \text{ psi} \] Enter "22.04" in the input box.**(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.)****Answer:**- Probability: [\[Input Box\]]**Explanation:**- Given the average tire pressure is 29 psi and standard deviation is 3 psi, we need to find the probability that tire pressure falls below 22.04 psi.- Convert the tire pressure value into a Z-score using the formula: \[ Z = \frac{X - \mu}{\sigma} \] where \(X = 22.04\), \(\mu = 29\), and \(\sigma = 3\): \[ Z = \frac{22.04 - 29}{3} = \frac{-6.96}{3} = -2.32 \] Using the Z-table, find the probability corresponding to \(Z = -2.32\): \[ \text{Probability} \approx 0.0102 \] Enter "0.0102" in the input box.

Given that: Target tire pressure = 30 psi Standard deviation, σ=3 psi

Answered: Tire pressure monitoring systems (TPMS)…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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