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 28 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 20.16 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 .0045 (c) The manufacturer's recommended correct inflation range is 26 psi to 30 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

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 28 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 20.16 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 .0045 (c) The manufacturer's recommended correct inflation range is 26 psi to 30 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

Name: ---### Educational Material: Tire Pressure Monitoring Systems (TPMS)#
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Description: ---### Educational Material: Tire Pressure Monitoring Systems (TPMS)#### Homework: Chapter 7 (Sections 7.1 through 7.4)---#### Problem Statement:Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 28% bel

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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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

---

### Educational Material: Tire Pressure Monitoring Systems (TPMS)

#### Homework: Chapter 7 (Sections 7.1 through 7.4)

---

#### Problem Statement:

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 28 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.*

- Formula: $ \text{Warning Pressure} = \text{Target Pressure} \times (1 - \frac{28}{100}) $

- When the tire pressure is: [below / dropdown menu options] 2016 psi (input box)
- Answer: (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.*

- Probability: 0.0045 (input box)

(c) **The manufacturer's recommended correct inflation range is 26 psi to 30 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: (input box)

---

#### Explanation:

1. **TPMS Warning Pressure Calculation:**

- To calculate the pressure at which the TPMS will trigger a warning, the target pressure is multiplied by 72% (which is 100% - 28%).
- Example Calculation: $ 28 \times 0.72 = 20.16 $ psi

2. **Probability of Warning Trigger:**

- Given the normal distribution of tire pressures with mean (μ) = target pressure (28 psi) and standard deviation (σ) = 3 psi.
- Using Z-scores and normal distribution tables, the probability of the tire pressure dropping below the warning threshold can be computed.

3. **Probability of Recommended Inflation Range:**

- Calculate the probability that the tire pressure falls within 26 psi to 30 psi.
- Use the cumulative distribution function (CDF) for

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