Central Limit Theorem


TinkerPlots provides an excellent modeling environment to illustrate the Central Limit Theorem.
The notation for the normal distribution is N (population mean, standard deviation)
The notation for the standard normal distribution is N(0,1)

Central Limit Theorem
Draw an SRS of size n from ANY population with mean mu and a finite standard deviation of sigma. When n is large, the sampling distribution of the sample mean is approximately Normal.
CLT from a different source
As the sample size n increases without limit, the shape of the distribution of the sample means taken with replacement from a population with mean mu and standard deviation sigma will approach a normal distribution. This distribution will have a mean mu and standard deviation [sigma / sqrt(n) ].

Oven Repair
If 42 ovens are repaired, find the probability that the mean of the repair bills will be greater than $57.
The steps for creating the model in TinkerPlots are shown in this activity.



Shower Time
Find the probability that the mean time of a random sample of 35 Americans who shower is greater than 14 minutes.
The steps for creating the model in TinkerPlots are shown in this activity. Also, this problem looks at a situation were the probability is zero.