Question

the given contingency table lists the cross tabulation of whether adults, for whom answering the question was appropriate, feel their life is exciting, routine, or dull for males and females among the 1,878 appropriate adults in a certain country. using the letters given in the table, find the number of respondents in each of the following sets in parts (a) through (d). (a) e contains 955 respondents. (simplify your answer.) (b) r ∩ f contains 470 respondents. (simplify your answer.) (c) e ∪ m contains 1353 respondents. (simplify your answer.) (d) e contains □ respondents. (simplify your answer.)

Explanation:

Step1: Recall the formula for complement

The complement of a set \(E\), denoted as \(E'\), contains all elements that are not in \(E\). The total number of respondents \(n(T)=1878\).

Step2: Find \(n(E)\)

From part (a), \(n(E) = 437+518=955\)

Step3: Calculate \(n(E')\)

Using the formula \(n(E')=n(T)-n(E)\)
Substitute \(n(T) = 1878\) and \(n(E)=955\)
\(n(E')=1878 - 955\)
\(n(E')=923\)

Answer:

\(923\)