Question

List and discuss at least three variables from everyday life for which you expect the variable  x  itself  not  to follow a normal or bell-shaped distribution. Then discuss what would happen to the sampling distribution  x  if the sample size were increased. 

Answer 1

1. Number of accidents in a town: The number of accidents does not follow the normal distribution instead it follows Poisson distribution. A poisson distribution is best apply where the avearge is very less and n is very large. No. of accidents also occur using this because average no. of scidents are vary less and population is very high. Also the poisson is a discrete distribution while Normal is continuous distribution.

2. No. of orders recieved in a restaurant, no.of orders recieved in an hoare discrete and it also follows the poisson distribution.

3. In a city 60% people own car a car and you selected 10 people randomly. X is the no. of people own a car. It follows the Binomial distribution because n i definite and p is same for all. Each person is independent of other.

Now, what if the sample size does not increase then the application of central limit thoerem will not be possible because it applies when the sample is enough large.