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 hub for a great deal of statistical work. 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.

In depth, 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.)

*please explain each one*

Solution

An example would be how many gas miles an average household uses in a given week because some familys commute further away from their home than others.

This would have a behavior depends in how many people live further away and closer

or if the city is small or big , it depends in a lot of things

Another example might be how many customers a restaurant has in a given day. There are many variables that could sway the results making the information a little less reliable.

this can be a poisson distribution because the customer arrive at certain mean or rate

and the employees have a rate for attendence the customer that arrived

another example is the time that you spend in a certain place like in a bank, or in a burger king to order,

the time that you spend to order is not normally distrited because they have or would have a mean that have a behavior like a poisson distribution