Questions: James is interested in the relationship between weather conditions and whether the downtown train he sometimes takes runs on time. For a year, James records whether each day is sunny, cloudy, rainy, or snowy, as well as whether this train arrives on time or is delayed. His results are displayed in the table below. Weather condition On time Delayed Total Sunny 167 3 170 Cloudy 115 5 120 Rainy 40 15 55 Snowy 8 12 20 Total 330 35 365 Which graph displays the conditional distributions of arrival status for each weather condition?

James is interested in the relationship between weather conditions and whether the downtown train he sometimes takes runs on time. For a year, James records whether each day is sunny, cloudy, rainy, or snowy, as well as whether this train arrives on time or is delayed. His results are displayed in the table below. Weather condition On time Delayed Total Sunny 167 3 170 Cloudy 115 5 120 Rainy 40 15 55 Snowy 8 12 20 Total 330 35 365 Which graph displays the conditional distributions of arrival status for each weather condition?
Transcript text: James is interested in the relationship between weather conditions and whether the downtown train he sometimes takes runs on time. For a year, James records whether each day is sunny, cloudy, rainy, or snowy, as well as whether this train arrives on time or is delayed. His results are displayed in the table below. \begin{tabular}{llll} \hline Weather condition & On time & Delayed & Total \\ \hline Sunny & 167 & 3 & 170 \\ \hline Cloudy & 115 & 5 & 120 \\ \hline Rainy & 40 & 15 & 55 \\ \hline Snowy & 8 & 12 & 20 \\ \hline Total & 330 & 35 & 365 \\ \hline \end{tabular} Which graph displays the conditional distributions of arrival status for each weather condition?
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Solution

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Solution Steps

Step 1: Understand the Problem

James is analyzing the relationship between weather conditions and the punctuality of a downtown train. The data provided includes the number of times the train was on time or delayed under different weather conditions (sunny, cloudy, rainy, snowy).

Step 2: Identify the Data

The table provides the following data:

  • Sunny: On time = 167, Delayed = 170
  • Cloudy: On time = 115, Delayed = 55
  • Rainy: On time = 33, Delayed = 15
  • Snowy: On time = 15, Delayed = 35
Step 3: Calculate Conditional Distributions

To find the conditional distributions of arrival status for each weather condition, calculate the percentage of on-time and delayed trains for each weather condition.

Sunny:
  • Total: 167 + 170 = 337
  • On time: (167 / 337) * 100 ≈ 49.6%
  • Delayed: (170 / 337) * 100 ≈ 50.4%
Cloudy:
  • Total: 115 + 55 = 170
  • On time: (115 / 170) * 100 ≈ 67.6%
  • Delayed: (55 / 170) * 100 ≈ 32.4%
Rainy:
  • Total: 33 + 15 = 48
  • On time: (33 / 48) * 100 ≈ 68.8%
  • Delayed: (15 / 48) * 100 ≈ 31.2%
Snowy:
  • Total: 15 + 35 = 50
  • On time: (15 / 50) * 100 = 30%
  • Delayed: (35 / 50) * 100 = 70%
Step 4: Match the Graph

Compare the calculated percentages with the graphs provided to determine which graph correctly displays the conditional distributions.

Final Answer

The first graph correctly displays the conditional distributions of arrival status for each weather condition.

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