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

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

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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Question

100%

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.

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---

### 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

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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

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