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Central limit theorem
- Intro Lesson: a18:29
- Intro Lesson: b9:57
- Lesson: 1a6:35
- Lesson: 1b9:40
- Lesson: 1c5:48
- Lesson: 27:32
- Lesson: 3a6:07
- Lesson: 3b6:04
- Lesson: 3c9:22
Central limit theorem
Lessons
The distribution of sampling means is normally distributed
⋅ μx=μ
⋅ σx=nσ
Central Limit Theorem:
Z=σxx−μx=nσx−μ
Typically n≥30
⋅ μx=μ
⋅ σx=nσ
Central Limit Theorem:
Z=σxx−μx=nσx−μ
Typically n≥30
- Introductiona)The distribution of sampling means is normally distributedb)Formula for the Central Limit Theorem
- 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.a)Find the probability that a randomly selected car will weigh more than 1400kg.b)What is the probability that a group of 30 cars will have an average weight of more than 1400kg?c)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? - 3.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%.a)If 20 students are randomly sampled what is the probability that the average of their mark is above 72%?b)If 50 students are randomly sampled what is the probability that the average of their mark is above 72%?c)If 100 students are randomly sampled what is the probability that the average of their mark is above 72%?