Asked by Braeden Moody on Jun 24, 2024
Verified
A population consists of 15 items.The number of different simple random samples of size 3 that can be selected from this population is
A) 45.
B) 455.
C) 3375.
D) 2730.
Simple Random Samples
A subset of individuals chosen from a larger set, where each individual is chosen randomly and entirely by chance.
Population
The entire pool from which a statistical sample is drawn and to which the results of analysis will be generalized.
- Ascertain the number of viable simple random samples that could be selected from an established population size.
Verified Answer
DK
Dennell KrebsJun 30, 2024
Final Answer :
B
Explanation :
The number of different simple random samples of size 3 that can be selected from a population of 15 items is calculated using the combination formula C(n,k)=n!k!(n−k)!C(n, k) = \frac{n!}{k!(n-k)!}C(n,k)=k!(n−k)!n! , where nnn is the total number of items in the population (15 in this case) and kkk is the size of each sample (3 in this case). Therefore, C(15,3)=15!3!(15−3)!=15!3!12!=15×14×133×2×1=455C(15, 3) = \frac{15!}{3!(15-3)!} = \frac{15!}{3!12!} = \frac{15 \times 14 \times 13}{3 \times 2 \times 1} = 455C(15,3)=3!(15−3)!15!=3!12!15!=3×2×115×14×13=455 .
Learning Objectives
- Ascertain the number of viable simple random samples that could be selected from an established population size.