What is the Probability of Getting 16 Yes Answers in a Small Population Survey?

Click For Summary
SUMMARY

The probability of obtaining 16 'Yes' answers from a survey of 20 individuals out of a total population of 35 is calculated using binomial probability. The analysis indicates that the likelihood of the remaining 15 individuals answering 'No' is 0.003%. This calculation assumes that the probability of answering 'Yes' or 'No' is equal among those not surveyed. The discussion highlights the importance of understanding binomial distributions in small population surveys.

PREREQUISITES
  • Understanding of binomial probability distribution
  • Familiarity with basic statistical concepts
  • Knowledge of survey sampling techniques
  • Ability to perform probability calculations
NEXT STEPS
  • Study binomial probability formulas and applications
  • Learn about survey design and sampling methods
  • Explore statistical software for probability calculations
  • Investigate the implications of small sample sizes in statistics
USEFUL FOR

Statisticians, survey researchers, data analysts, and anyone involved in designing or interpreting survey results in small populations.

moonman239
Messages
276
Reaction score
0
Let's say I survey 20 people out of a 35-person population. 16 people answered yes to a particular question. What is the probability that only 16 people out of the total population would answer yes?

Attempt at a solution: The number of those not surveyed have an equal
probability of answering yes or no. Thus the probability of
those not surveyed all answering no is .003%.
 
Physics news on Phys.org
How did you get 0.003%?

What is the probability that any given individual will answer 'yes'?
How many people are remaining?
 

Similar threads

Probability Word Problem: Aptitude Question
  • · Replies 8 ·
Replies
8
Views
3K
What is the ideal number of guesses to maximize your marks in MCQs?
  • · Replies 29 ·
Replies
29
Views
3K
Probability: Dice Game between 20- and 12-sided dice with re-rolls
  • · Replies 2 ·
Replies
2
Views
2K
Choose a ball at random from a randomly selected box - alternative way
  • · Replies 10 ·
Replies
10
Views
3K
Probability of getting a Four-of-a-kind?
  • · Replies 7 ·
Replies
7
Views
2K
Find probability of certain event, total probability theorem
  • · Replies 6 ·
Replies
6
Views
2K
Probability of Getting a Total of 15 or Higher in Three Dice Throws
  • · Replies 1 ·
Replies
1
Views
3K
M&Ms Probability Help: Understanding P(B|A) in Random Selection Scenarios"
  • · Replies 9 ·
Replies
9
Views
2K
Conditional Probability Question
  • · Replies 6 ·
Replies
6
Views
3K
Probability that both people are from group X
  • · Replies 18 ·
Replies
18
Views
2K