Answer :
To find the expected number of students doing 3 fine arts courses in the larger group of 430 students, we can use the concept of proportions from statistics.
Define the Sample Proportion:
From the sample of 20 students, 12 of them are doing 3 fine arts courses. The proportion [tex]p[/tex] of students in the sample doing 3 fine arts courses is:
[
p = \frac{12}{20} = 0.6
]
Apply the Proportion to the Population:
To estimate the expected number of students doing 3 fine arts courses in the whole group of 430 students, we multiply the total number of students by the sample proportion:
[
\text{Expected number} = 0.6 \times 430 = 258
]
Therefore, the expected number of students doing 3 fine arts courses in the group of 430 students is 258.
This calculation assumes that the sample of 20 students is representative of the entire population of 430 students. The process used here is based on the principle of statistical inference, where characteristics of a sample are used to estimate characteristics of a larger population.
