Questions: Your daily commute to work requires that you cross railroad tracks. At this particular railroad crossing the trains tend to be long and slow, So, getting stopped by a train will likely make you late for work. You start recording data to determine the likelihood of arriving at the tracks while a train is there. The data contain the day number and whether a train was present, or not, for 200 consecutive days in which you drove to work in the data set, the column Train shows a series of 0s and 1s. In that column a 0 indicates there was no train present and a 1 indicates that a train was present. The column Aggregate Train represents the cumulative number of times a train was present. Consider the first 10 days of data. For this time period, what proportion of days had a train present? (Round to four decimal places as needed)

Your daily commute to work requires that you cross railroad tracks. At this particular railroad crossing the trains tend to be long and slow, So, getting stopped by a train will likely make you late for work. You start recording data to determine the likelihood of arriving at the tracks while a train is there. The data contain the day number and whether a train was present, or not, for 200 consecutive days in which you drove to work in the data set, the column Train shows a series of 0s and 1s. In that column a 0 indicates there was no train present and a 1 indicates that a train was present. The column Aggregate Train represents the cumulative number of times a train was present.

Consider the first 10 days of data. For this time period, what proportion of days had a train present? 
(Round to four decimal places as needed)
Transcript text: Your daily commute to work requires that you cross railroad tracks. At this particular railroad crossing the trains tend to be long and slow, So, getting stopped by a train will likely make you late for work. You start recording data to determine the likelihood of arriving at the tracks while a train is there. The data contain the day number and whether a train was present, or not, for 200 consecutive days in which you drove to work in the data set, the column Train shows a series of 0s and 1s. In that column a 0 indicates there was no train present and a 1 indicates that a train was present. The column Aggregate Train represents the cumulative number of times a train was present. Consider the first 10 days of data. For this time period, what proportion of days had a train present? $\square$ (Round to four decimal places as needed)
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Solution

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Solution Steps

Step 1: Count the Number of Days a Train Was Present

To find the number of days a train was present, we sum the values in the train_data list. Each 1 represents a day when a train was present.

\[ \text{train\_present\_days} = 1 + 0 + 1 + 1 + 0 + 0 + 1 + 0 + 1 + 1 = 6 \]

Step 2: Determine the Total Number of Days

The total number of days in the given period is the length of the train_data list.

\[ \text{total\_days} = 10 \]

Step 3: Calculate the Proportion of Days with a Train Present

The proportion of days with a train present is calculated by dividing the number of days a train was present by the total number of days.

\[ \text{proportion\_train\_present} = \frac{\text{train\_present\_days}}{\text{total\_days}} = \frac{6}{10} = 0.6 \]

Final Answer

The proportion of days with a train present over the first 10 days is \(\boxed{0.6}\).

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