The central angle be for this category is A. 198 degrees
The 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 is the number of ways to arrange objects.
[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]
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]
Grade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation
Answer: A. 198 degrees
Step-by-step explanation:
Given : The proportion of students worked at least sometime during their undergraduate career = 87%= 0.87
The proportion of the students worked throughout their undergraduate career= 32%=0.32
Now, the proportion of the students who worked sometime during their undergraduate career, but not throughout. = 0.87- 0.32= 0.55
For pie chart the central angle would be :-
[tex]\text{Proportion of required category}\times 360^{\circ}\\\\=0.55\times360^{\circ}\\\\=198^{\circ}[/tex]
Hence, the central angle be for this category = 198 degrees
