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 31 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 psi. below (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 29 psi to 33 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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**Title: Understanding Tire Pressure Monitoring Systems (TPMS) and Probability Calculations**

Tire pressure monitoring systems (TPMS) alert 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 31 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:** [below] ___ 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 29 psi to 33 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:** [ ]

This exercise involves understanding the function of TPMS and applying statistical concepts involving normal distribution and probability to practical scenarios.
Transcribed Image Text:**Title: Understanding Tire Pressure Monitoring Systems (TPMS) and Probability Calculations** Tire pressure monitoring systems (TPMS) alert 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 31 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:** [below] ___ 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 29 psi to 33 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:** [ ] This exercise involves understanding the function of TPMS and applying statistical concepts involving normal distribution and probability to practical scenarios.
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