1. What are the assumptions underlying a normal distribution?
2. What are the assumptions underlying a binomial distribution?
3. Why do we want to assume that our sample data represent a
4. What are the differences between the binomial and normal
5. What are the similarities between the binomial and normal
Here are answers to your questions:
In many cases, it is appropriate to summarize a group of independent observations by the number of observations in the group that represent one of two outcomes. For example, the proportion of individuals in a random sample who support one of two political candidates fits this description. In this case, the statistic is the count X of voters who support the candidate divided by the total number of individuals in the group n. This provides an estimate of the parameter p, the proportion of individuals who support the candidate in the entire population.
The binomial distribution describes the behavior of a count variable X if the following conditions apply:
1: The number of observations n is fixed.
2: Each observation is independent.
3: Each observation represents one of two outcomes ("success" or "failure").
4: The probability of "success" p is the same for each outcome.
If these conditions are met, then X has a binomial distribution with parameters n and p, abbreviated B(n,p).
Suppose individuals with a ...