In one way the central limit theorem can be thought of as a

In one way, the central limit theorem can be thought of as a kind of \"grand central station.\" It is a connecting nub for a great deal of statistical work. We will use it extensively in the remaining modules. Put in simpler terms, the central limit theorem states that as the sample size n increases, the distribution of the sample mean x with minus on top will always approach a normal distribution, no matter where the original x variable came from. For most people, it is the complete generality of the central limit theorem that is so amazing: it applies to almost everything.

For this project, 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. In your discussion you should include the following:

For each variable in detail: 1) Describe the variable 2) Why you don\'t think the variable is normally distributed 3) What you expect the distribution to be (for example, right skewed, left skewed, bimodal, etc.)

Solution

#1 House Prices: Let variable X denotes the house price in USA. This variable canot be normally distributed because house prices depends on several factors like locality, area etc. Some of the houses would be extremely costly. Therefore, the distribution of house prices would be positively skewed.

#2 Number of accidents: Let variable X denotes the number of accidents in USA. This variable canot be normally distributed because this is discrete variable. This variable woild follow Poisson distribution because n is very large and probability of success is very small.

#3 Number of heads in 100 tosses: Let variable X denotes the number of heads in 100 tosses. This variable canot be normally distributed because this is discrete variable. This variable woild follow Binomial distribution because tosses are independent, n is fixed and probability of success is same in each toss (trial).