4. Explain the binomial probability distribution with examples.
Answers
Answer:
The binomial distribution is often used in social science statistics as a building block for models for dichotomous outcome variables, like whether a Republican or Democrat will win an upcoming election or whether an individual will die within a specified period of time, etc.
Analyzing Binomial Distribution:
The expected value, or mean, of a binomial distribution, is calculated by multiplying the number of trials by the probability of successes. For example, the expected value of the number of heads in 100 trials of head and tales is 50, or (100 * 0.5). Another common example of the binomial distribution is by estimating the chances of success for a free-throw shooter in basketball where 1 = a basket is made and 0 = a miss.
Example of Binomial Distribution:
The binomial distribution is calculated by multiplying the probability of success raised to the power of the number of successes and the probability of failure raised to the power of the difference between the number of successes and the number of trials. Then, multiply the product by the combination between the number of trials and the number of successes.
For example, assume that a casino created a new game in which participants are able to place bets on the number of heads or tails in a specified number of coin flips. Assume a participant wants to place a $10 bet that there will be exactly six heads in 20 coin flips. The participant wants to calculate the probability of this occurring, and therefore, they use the calculation for the binomial distribution.