# Central limit theorem

##### Intros
###### Lessons
1. The distribution of sampling means is normally distributed
2. Formula for the Central Limit Theorem
##### Examples
###### Lessons
1. Comparing the Individual Z-Score to the Central Limit Theorem
A population of cars has an average weight of 1350kg with a standard deviation of 200 kg. Assume that these weights are normally distributed.
1. Find the probability that a randomly selected car will weigh more than 1400kg.
2. What is the probability that a group of 30 cars will have an average weight of more than 1400kg?
3. Compare the two answers found in the previous parts of this question.
2. Applying the Central Limit Theorem
Skis have an average weight of 11 lbs, with a standard deviation of 4 lbs. If a sample of 75 skis is tested, what is the probability that their average weight will be less than 10 lbs?
1. Increasing Sample Size
At the University of British Columbia the average grade for the course "Mathematical Proofs" is 68%. This grade has a standard deviation of 15%.
1. If 20 students are randomly sampled what is the probability that the average of their mark is above 72%?
2. If 50 students are randomly sampled what is the probability that the average of their mark is above 72%?
3. If 100 students are randomly sampled what is the probability that the average of their mark is above 72%?