Question

Give your own example of a situation in which each of the following distributions would apply and explain how it fits the distribution:

a. Uniform distribution

b. Normal distribution

c. Binomial distribution

d. Normal approximation of the binomial distribution

Answer 1

a) Uniform distribution

It is used for generate the random numbers from the population

b) Normal distribution

Many of the distribution of errors ( actual - estimate) follows normal distribution.

And so we can use it in regression, ANOVA for model diagnostic.

c) Binomial distribution

If the wining probability of a football game in a league matches of a particular team is 0.7

Then by using Binomial distribution we can find the probability of winning of the games.

d) Normal approximation of the binomial distribution.

When n = number of trial are very large then we can use Normal approximation of the binomial distribution to find the probabilities.

For example: In a batch of 1000 items if probability of defective of the item = 0.3 then we can use Normal approximation of the binomial distribution for finding probabilities of different events such as

P( less than 200 items are defectives out of 1000 items)

P( at most 230 items are defectives out of 1000 items) and so on