Dirty air: The federal government has enacted maximum allowable standards for air pollutants such as ozone. Let X be the of days per year that the level of air pollution exceeds the standard in a certain city. The probability distribution of X is given 1 2 3 P(x) 0.35 0.38 0.19 0.05 0.03 X Send data to Excel Part 1 of 4 (a) Find P (3). P(3)= 0.05 Part 2 of 4 0 (b) Find P (3 or fewer). P (3 or fewer) = 0.97 Part 3 of 4 Part: 3/4 (c) Find the probability that the standard is exceeded on at least two days. The probability that the standard is exceeded on at least two days is 0.27 Part 4 of 4 4 (d) Find the probability that the standard is exceeded on more than two days. The probability that the standard is exceeded on more than two days is

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Dirty air: The federal government has enacted maximum allowable standards for air pollutants such as ozone. Let X be the number
of days per year that the level of air pollution exceeds the standard in a certain city. The probability distribution of X is given by
(→
1
2 3 4
P(x) 0.35 0.38 0.19 0.05 0.03
X
Send data to Excel
Part 1 of 4
(a) Find P (3).
P (3)= 0.05
Part 2 of 4
0
(b) Find P (3 or fewer).
P (3 or fewer) = 0.97
Part 3 of 4
(c) Find the probability that the standard is exceeded on at least two days.
The probability that the standard is exceeded on at least two days is 0.27
Part: 3/4
Part 4 of 4
(d) Find the probability that the standard is exceeded on more than two days.
The probability that the standard is exceeded on more than two days is
B
V
Transcribed Image Text:Dirty air: The federal government has enacted maximum allowable standards for air pollutants such as ozone. Let X be the number of days per year that the level of air pollution exceeds the standard in a certain city. The probability distribution of X is given by (→ 1 2 3 4 P(x) 0.35 0.38 0.19 0.05 0.03 X Send data to Excel Part 1 of 4 (a) Find P (3). P (3)= 0.05 Part 2 of 4 0 (b) Find P (3 or fewer). P (3 or fewer) = 0.97 Part 3 of 4 (c) Find the probability that the standard is exceeded on at least two days. The probability that the standard is exceeded on at least two days is 0.27 Part: 3/4 Part 4 of 4 (d) Find the probability that the standard is exceeded on more than two days. The probability that the standard is exceeded on more than two days is B V
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Follow-up Question
**Title: Understanding Probability Distribution of Pollution Standard Exceedance**

**Introduction:**
The federal government has set maximum allowable standards for air pollutants, such as ozone. This exercise explores the probability distribution of \( X \), the number of days per year that the level of air pollution exceeds the standard in a certain city.

**Probability Distribution Table:**

\[
\begin{array}{c|ccccc}
X & 0 & 1 & 2 & 3 & 4 \\
\hline
P(X) & 0.34 & 0.39 & 0.19 & 0.05 & 0.03 \\
\end{array}
\]

**Exercises:**

**Part 1 of 6**

(a) *Find \( P(1) \).*

\[
P(1) = 0.39
\]

**Part 2 of 6**

(b) *Find \( P(3 \text{ or fewer}) \).*

\[
P(3 \text{ or fewer}) = 0.97
\]

**Part 3 of 6**

(c) *Find the probability that the standard is exceeded on at least two days.*

\[
\text{The probability that the standard is exceeded on at least two days is } 0.27.
\]

**Part 4 of 6**

(d) *Find the probability that the standard is exceeded on more than two days.*

\[
\text{The probability that the standard is exceeded on more than two days is } 0.08.
\]

**Part 5 of 6**

(e) *Compute the mean \( \mu_X \). Round the answer to two decimal places.*

\[
\mu_X = \Box
\]

**Conclusion:**
This exercise demonstrates how to interpret and calculate probabilities from a given probability distribution for environmental data on pollution standards. Understanding these distributions helps in assessing compliance with environmental regulations.
Transcribed Image Text:**Title: Understanding Probability Distribution of Pollution Standard Exceedance** **Introduction:** The federal government has set maximum allowable standards for air pollutants, such as ozone. This exercise explores the probability distribution of \( X \), the number of days per year that the level of air pollution exceeds the standard in a certain city. **Probability Distribution Table:** \[ \begin{array}{c|ccccc} X & 0 & 1 & 2 & 3 & 4 \\ \hline P(X) & 0.34 & 0.39 & 0.19 & 0.05 & 0.03 \\ \end{array} \] **Exercises:** **Part 1 of 6** (a) *Find \( P(1) \).* \[ P(1) = 0.39 \] **Part 2 of 6** (b) *Find \( P(3 \text{ or fewer}) \).* \[ P(3 \text{ or fewer}) = 0.97 \] **Part 3 of 6** (c) *Find the probability that the standard is exceeded on at least two days.* \[ \text{The probability that the standard is exceeded on at least two days is } 0.27. \] **Part 4 of 6** (d) *Find the probability that the standard is exceeded on more than two days.* \[ \text{The probability that the standard is exceeded on more than two days is } 0.08. \] **Part 5 of 6** (e) *Compute the mean \( \mu_X \). Round the answer to two decimal places.* \[ \mu_X = \Box \] **Conclusion:** This exercise demonstrates how to interpret and calculate probabilities from a given probability distribution for environmental data on pollution standards. Understanding these distributions helps in assessing compliance with environmental regulations.
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Follow-up Question
The image displays a section from an educational platform interface, specifically a task involving statistical calculations. Here is a transcription of the content suitable for an educational website:

---

### Compute the Mean \( \mu_X \)

**Part 5 of 6**

\( (e) \) Compute the mean \( \mu_X \). Round the answer to two decimal places.

- Input field for \( \mu_X \)
- Controls: A button with an "X" and a button with a circular arrow, likely for clearing the input or resetting.

**Navigation and Copyright**

- "Next Part" button for progressing to the next section.
- Footer notes © 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy

---

This section guides learners through the process of calculating the mean of a dataset, emphasizing accuracy by instructing them to round to two decimal places.
Transcribed Image Text:The image displays a section from an educational platform interface, specifically a task involving statistical calculations. Here is a transcription of the content suitable for an educational website: --- ### Compute the Mean \( \mu_X \) **Part 5 of 6** \( (e) \) Compute the mean \( \mu_X \). Round the answer to two decimal places. - Input field for \( \mu_X \) - Controls: A button with an "X" and a button with a circular arrow, likely for clearing the input or resetting. **Navigation and Copyright** - "Next Part" button for progressing to the next section. - Footer notes © 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy --- This section guides learners through the process of calculating the mean of a dataset, emphasizing accuracy by instructing them to round to two decimal places.
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Follow-up Question
The probability that the standard is exceeded on more than two days is 0.08.

Part: 4 / 6

Part 5 of 6

(e) Compute the mean \( \mu_X \). Round the answer to two decimal places.

\[ \mu_X = \, \]

[ ]  (Placeholder for input)

[Button with X symbol] [Button with circular arrow symbol]

Next Part

© 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center
Transcribed Image Text:The probability that the standard is exceeded on more than two days is 0.08. Part: 4 / 6 Part 5 of 6 (e) Compute the mean \( \mu_X \). Round the answer to two decimal places. \[ \mu_X = \, \] [ ] (Placeholder for input) [Button with X symbol] [Button with circular arrow symbol] Next Part © 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center
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