Question

1. What makes the binomial distribution unique? What are its characteristics?

Give a real-world example of a distribution of data that would be considered binomial.

2. Solve the following problem:
About 30% of adults in United States have college degree.
(probability that a person has college degree is p = 0.30).

If N adults are randomly selected, find probabilities that

1) exactly X out of selected N adults have college degree
2) less than X out of selected N adults have college degree
3) greater than X out of selected N adults have college degree

Choose your numbers for N and X.

Answer 1

Binomial distribution only takes into account two states , success or failure , where probability of success is constant for each trial , this property makes the Binomial distribution unique.

The characteristics of Binomial distribution

1. Number of trials n is finite

2. Trials are independent of each other

3. Each trial has two outcomes , success or failure

4. The probability of success is constant for each trial

Example:

Suppose 76% of the business startups in restaurant industry report that they generate profit in the first year.A random sample of 10 new restaurant is selected, let X be the number of new restaurants who generate profit . Then distribution of X follow Binomial with n = 10(number of trials) , p = 0.76( the probability of success)

2. p = 0.30

1.probability of exactly x out of n selected adults

let n = 20 , x = 5

2.less than x out of selected n

= 0.2375

3.