A survey question revealed that at a particular college 87 percent of students worked at least sometime during their undergraduate career and 13 percent did not work at all. Another question showed that 32 percent of the students worked throughout their undergraduate career. A pie chart is created that includes the category "Students who worked sometime during their undergraduate career, but not throughout." What would the central angle be for this category? A. 198 degrees B. 47 degrees C. 313 degrees D. 115 degrees

The central angle be for this category is A. 198 degreesFurther explanationThe probability of an event is defined as the possibility of an event occurring against sample space.[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]Permutation ( Arrangement )Permutation is the number of ways to arrange objects.[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]Combination ( Selection )Combination is the number of ways to select objects.[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]Let us tackle the problem.This problem is about Percentage.32 percent of the students worked throughout their undergraduate career.[tex]\texttt{Percentage of Students Worked throughout their undergraduate career} = 32 \%[/tex][tex]\texttt{ }[/tex]A survey question revealed that at a particular college 87 percent of students worked at least sometime during their undergraduate career.[tex]\texttt{Percentage of Students Worked sometime but not throughout} = 87 \% - 32 \%[/tex][tex]\texttt{Percentage of Students Worked sometime but not throughout} = 55 \%[/tex][tex]\texttt{ }[/tex]Since the angle of 1 rotation is 360 degrees , then:[tex]\texttt{Central Angle for this category} = 55 \% \times 360^o[/tex][tex]\texttt{Central Angle for this category} = \frac{55}{100} \times 360^o[/tex][tex]\texttt{Central Angle for this category} = \frac{11}{20} \times 360^o[/tex][tex]\texttt{Central Angle for this category} = 11 \times \frac{360^o}{20}[/tex][tex]\texttt{Central Angle for this category} = 11 \times 18^o[/tex][tex]\texttt{Central Angle for this category} = 198^o[/tex][tex]\texttt{ }[/tex]Learn moreDifferent Birthdays : or Independent Events : exclusive : detailsGrade: High SchoolSubject: MathematicsChapter: ProbabilityKeywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation