I only need help with "D" i only need help with "D" thank you! ### Commuter Data Analysis**1. Commuter Statistics in Massachusetts (2015)**The table below presents data on commuters in Massachusetts in 2015, categorized by transportation method and the duration of a one-way commute. The numbers are given in thousands.| Commute Time | < 15 min | 15-29 min | 30-44 min | 44-59 min | 60 min or more | Total ||-------------------|----------|-----------|-----------|-----------|----------------|-------|| **Private Vehicle** | 636 | 908 | 590 | 257 | 256 | 2647 || **Public Transport**| 9 | 54 | 96 | 62 | 108 | 329 || **Other** | 115 | 70 | 23 | 7 | 7 | 222 || **Total** | 760 | 1032 | 709 | 326 | 371 | 3198 |**Calculations:**- **a) Probability of using a private vehicle and having a 15-29 min commute:** Formula: $ P(\text{private vehicle and 15-29 min commute}) = \frac{908}{3198} \approx 0.284 $- **b) Probability of using a private vehicle times the probability of a 15-29 min commute:** Formula: \[ P(\text{private vehicle}) \times P(\text{15-29 min commute}) = \frac{2647}{3198} \times \frac{1032}{3198} \approx 0.267 \]- **c) Independence Analysis:** Determine if using a private vehicle and having a 15-29 min commute are independent: **Independent Formula:** \[ P(\text{private vehicle and 15-29 min commute}) = P(\text{private vehicle}) \times P(\text{15-29 min commute}) \] **Not Independent:** From calculations, the values differ, so having a private vehicle and a 15-29 min commute are not independent events.**d) Question on Independence:**- **How do you know?** Compare the product **Table of Commuter Data in Massachusetts (2015)**The table below shows the number of commuters in Massachusetts in 2015 (in thousands) categorized by the mode of transportation and one-way commute length.| | < 15 min | 15-29 min | 30-44 min | 44-59 min | 60 min or > | Total ||--------------|----------|-----------|-----------|-----------|-------------|--------|| Private Vehicle | 636 | 908 | 590 | 257 | 256 | 2647 || Public Transport | 9 | 54 | 96 | 62 | 108 | 329 || Other | 115 | 70 | 23 | 7 | 7 | 222 || **Total** | **760** | **1032** | **709** | **326** | **371** | **3198**|**Calculations:**a) **P(private vehicle and 15-29 min commute)**- Formula: $ P(A \text{ and } B) = \frac{n(\text{private vehicle and 15-29 min commute})}{\text{total}} $ \[ P = \frac{908}{3198} = 0.2841 \]b) **P(private vehicle) x P(15-29 min commute)**- P(private vehicle): $ \frac{2647}{3198} = 0.82705 $- P(15-29 min commute): $ \frac{1032}{3198} = 0.322702 $- Combined Probability: \[ P = 0.82705 \times 0.322702 = 0.26710 \]c) **Independence Check:**- Two events are independent if: \[ P(\text{private vehicle and 15-29 min commute}) = P(\text{private vehicle}) \times P(\text{15-29 min commute}) \]- Calculation shows: \[ 0.2841 \neq 0.26710 \]- Hence, having a private vehicle and a 15-29 min commute time are **not independent

Step 1: Suppose that we have two events A and B. Then the two events are independent if the…

1. The table below gives the thousands of commuters in Massachusetts in 2015 by transportation method and one-way length of commute. < 15min 15-29min 30-44min 44-59min 60 or > total private vehicle 636 908 590 257 256 2647 public transport 9 54 96 62 108 329 other 115 70 23 7 222 Total 760 1032 709 326 371 3198 Find the following as decimals to the nearest thousandth: a) P(private vehicle and 15-29 min. commute) "and" is key =ncerivatevehicle and 15 908 にerd84 ろ1981 0.282 0.283931 to tal b) P(private vehicle) xP (15-29 min. commute ) =(Pr ?(Private vehicle) x e(15 -29 min, total = 2647 to tal 7 0.82770S x0,32270230.2 %3D 1032 3198 3198 =0.267 c) Based on your calculations, are having a private vehicle and a 15-29 min. commute time independent of one another? Google the formula for independent probability look for set notation. Independent : Plerivate vehicle and 15-29 min,com P(private venicle)xP(15-29min Commute frem Parts (A) and(6) Not Independent:P(Privale vehicle and15-39min commute): P(Private ehicle)xP(15aamin commute) Private venice and 15-29 min.commute are not D) How do you know? Can you make a formula for independent events using set notation? indeR

1. The table below gives the thousands of commuters in Massachusetts in 2015 by transportation method and one-way length of commute. < 15min 15-29min 30-44min 44-59min 60 or > total private vehicle 636 908 590 257 256 2647 public transport 9 54 96 62 108 329 other 115 70 23 7 222 Total 760 1032 709 326 371 3198 Find the following as decimals to the nearest thousandth: a) P(private vehicle and 15-29 min. commute) "and" is key =ncerivatevehicle and 15 908 にerd84 ろ1981 0.282 0.283931 to tal b) P(private vehicle) xP (15-29 min. commute ) =(Pr ?(Private vehicle) x e(15 -29 min, total = 2647 to tal 7 0.82770S x0,32270230.2 %3D 1032 3198 3198 =0.267 c) Based on your calculations, are having a private vehicle and a 15-29 min. commute time independent of one another? Google the formula for independent probability look for set notation. Independent : Plerivate vehicle and 15-29 min,com P(private venicle)xP(15-29min Commute frem Parts (A) and(6) Not Independent:P(Privale vehicle and15-39min commute): P(Private ehicle)xP(15aamin commute) Private venice and 15-29 min.commute are not D) How do you know? Can you make a formula for independent events using set notation? indeR

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Author:Amos Gilat

Publisher:Amos Gilat

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Question

I only need help with "D" i only need help with "D" thank you!

### Commuter Data Analysis

**1. Commuter Statistics in Massachusetts (2015)**

The table below presents data on commuters in Massachusetts in 2015, categorized by transportation method and the duration of a one-way commute. The numbers are given in thousands.

| Commute Time | < 15 min | 15-29 min | 30-44 min | 44-59 min | 60 min or more | Total |
|-------------------|----------|-----------|-----------|-----------|----------------|-------|
| **Private Vehicle** | 636 | 908 | 590 | 257 | 256 | 2647 |
| **Public Transport**| 9 | 54 | 96 | 62 | 108 | 329 |
| **Other** | 115 | 70 | 23 | 7 | 7 | 222 |
| **Total** | 760 | 1032 | 709 | 326 | 371 | 3198 |

**Calculations:**

- **a) Probability of using a private vehicle and having a 15-29 min commute:**

Formula:
$ P(\text{private vehicle and 15-29 min commute}) = \frac{908}{3198} \approx 0.284 $

- **b) Probability of using a private vehicle times the probability of a 15-29 min commute:**

Formula:
\[
P(\text{private vehicle}) \times P(\text{15-29 min commute}) = \frac{2647}{3198} \times \frac{1032}{3198} \approx 0.267
\]

- **c) Independence Analysis:**

Determine if using a private vehicle and having a 15-29 min commute are independent:

**Independent Formula:**
\[
P(\text{private vehicle and 15-29 min commute}) = P(\text{private vehicle}) \times P(\text{15-29 min commute})
\]

**Not Independent:**
From calculations, the values differ, so having a private vehicle and a 15-29 min commute are not independent events.

**d) Question on Independence:**

- **How do you know?** Compare the product

**Table of Commuter Data in Massachusetts (2015)**

The table below shows the number of commuters in Massachusetts in 2015 (in thousands) categorized by the mode of transportation and one-way commute length.

| | < 15 min | 15-29 min | 30-44 min | 44-59 min | 60 min or > | Total |
|--------------|----------|-----------|-----------|-----------|-------------|--------|
| Private Vehicle | 636 | 908 | 590 | 257 | 256 | 2647 |
| Public Transport | 9 | 54 | 96 | 62 | 108 | 329 |
| Other | 115 | 70 | 23 | 7 | 7 | 222 |
| **Total** | **760** | **1032** | **709** | **326** | **371** | **3198**|

**Calculations:**

a) **P(private vehicle and 15-29 min commute)**

- Formula: $ P(A \text{ and } B) = \frac{n(\text{private vehicle and 15-29 min commute})}{\text{total}} $

\[
P = \frac{908}{3198} = 0.2841
\]

b) **P(private vehicle) x P(15-29 min commute)**

- P(private vehicle): $ \frac{2647}{3198} = 0.82705 $

- P(15-29 min commute): $ \frac{1032}{3198} = 0.322702 $

- Combined Probability:

\[
P = 0.82705 \times 0.322702 = 0.26710
\]

c) **Independence Check:**

- Two events are independent if:

\[
P(\text{private vehicle and 15-29 min commute}) = P(\text{private vehicle}) \times P(\text{15-29 min commute})
\]

- Calculation shows:

\[
0.2841 \neq 0.26710
\]

- Hence, having a private vehicle and a 15-29 min commute time are **not independent

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