Question

here is a table giving the thousands of commuters in alabama in 2015 by transportation method and one - way duration of commute: commute duration (one - way) private vehicle public transportation other total < 15 minutes 498 1 27 526 15 - 29 minutes 748 2 8 758 30 - 44 minutes 387 2 4 393 45 - 59 minutes 145 1 0 146 ≥ 60 minutes 109 3 3 115 total 1887 9 42 1938 find the marginal distribution of one - way duration of commute in percentages. round to the nearest whole percent.

Explanation:

Step1: Recall the formula for percentage

The percentage of each commute - duration category is calculated as $\text{Percentage}=\frac{\text{Total for category}}{\text{Grand total}}\times100\%$. The grand total of commuters is $1938$ (in thousands).

Step2: Calculate percentage for $< 15$ minutes

For the $< 15$ minutes category, the total is $526$. The percentage is $\frac{526}{1938}\times100\%\approx 27\%$.

Step3: Calculate percentage for $15 - 29$ minutes

For the $15 - 29$ minutes category, the total is $758$. The percentage is $\frac{758}{1938}\times100\%\approx 39\%$.

Step4: Calculate percentage for $30 - 44$ minutes

For the $30 - 44$ minutes category, the total is $393$. The percentage is $\frac{393}{1938}\times100\%\approx 20\%$.

Step5: Calculate percentage for $45 - 59$ minutes

For the $45 - 59$ minutes category, the total is $146$. The percentage is $\frac{146}{1938}\times100\%\approx 8\%$.

Step6: Calculate percentage for $\geq60$ minutes

For the $\geq60$ minutes category, the total is $115$. The percentage is $\frac{115}{1938}\times100\%\approx 6\%$.

Answer:

$< 15$ minutes: $27\%$, $15 - 29$ minutes: $39\%$, $30 - 44$ minutes: $20\%$, $45 - 59$ minutes: $8\%$, $\geq60$ minutes: $6\%$