Tire 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.) (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 below psi. (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.) Probability
Tire 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.) (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 below psi. (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.) Probability
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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![### Tire Pressure Monitoring Systems (TPMS) Alert Parameters
#### Problem Context
Tire 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2883175-03e0-4ea8-b3e1-e40287ec9d26%2F55d882c6-1c8b-442d-81f1-8a7cded81fd0%2Fkbv00uc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Tire Pressure Monitoring Systems (TPMS) Alert Parameters
#### Problem Context
Tire 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.
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