Question

p. 15 conditional and joint relative frequencies. problem: in 1912 the luxury liner titanic, on its first voyage across the atlantic, struck an iceberg and sank. some passengers got off the ship in lifeboats, but many died. the two - way table gives information about adult passengers who survived and who died, by class of travel. survival status class of travel first second third survived 197 94 151 died 122 167 476 1.) what proportion of adult passengers survived? 2.) find the distribution of class of travel for adult passengers on the titanic using relative frequencies. 3.) what percent of adult titanic passengers traveled in third class and survived? 4.) what proportion of survivors were third - class passengers?

Explanation:

Step1: Calculate total number of adult passengers

The total number of adult passengers is the sum of all values in the table. So, \(197 + 94+151 + 122+167+476=1107\).

Step2: Calculate number of survivors

The number of survivors is \(197 + 94+151=442\).

Step3: Calculate proportion of survivors

The proportion of adult - passengers who survived is \(\frac{442}{1107}\approx0.399\).

Step4: Calculate relative frequencies for class of travel

The total number of first - class passengers is \(197 + 122 = 319\), the relative frequency of first - class passengers is \(\frac{319}{1107}\approx0.288\).
The total number of second - class passengers is \(94 + 167=261\), the relative frequency of second - class passengers is \(\frac{261}{1107}\approx0.236\).
The total number of third - class passengers is \(151+476 = 627\), the relative frequency of third - class passengers is \(\frac{627}{1107}\approx0.566\).

Step5: Calculate percentage of third - class survivors

The number of third - class survivors is 151. The percentage of adult Titanic passengers who traveled in third - class and survived is \(\frac{151}{1107}\times100\%\approx13.6\%\).

Step6: Calculate proportion of third - class survivors among all survivors

The proportion of third - class passengers among survivors is \(\frac{151}{442}\approx0.342\).

Answer:

1. The proportion of adult passengers who survived is approximately \(0.399\).
2. The relative frequencies for first - class, second - class, and third - class passengers are approximately \(0.288\), \(0.236\), and \(0.566\) respectively.
3. Approximately \(13.6\%\) of adult Titanic passengers traveled in third - class and survived.
4. The proportion of survivors who were third - class passengers is approximately \(0.342\).