What is a key application of the Central Limit Theorem discussed in the video?

Binomial Probability and Central Limit Theorem

Interactive Video
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Mathematics
•
11th - 12th Grade
•
Hard

Thomas White
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8 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Calculating exact probabilities of normal distributions
Finding the mode of a distribution
Approximating binomial probabilities
Determining the mean of a dataset
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What type of distribution do the random variables discussed in the video follow?
Bernoulli distribution
Poisson distribution
Normal distribution
Exponential distribution
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the Central Limit Theorem imply about the CDF of a standardized random variable as n approaches infinity?
It approaches the CDF of a standard normal distribution
It becomes undefined
It remains constant
It approaches the CDF of a uniform distribution
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example provided, what is the probability that SN is less than or equal to 21 using the binomial formula?
0.785
0.8785
0.5
0.9
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How does the approximation using the Central Limit Theorem compare to the exact calculation?
It is exactly the same
It is less accurate by about 10 percentage points
It is less accurate by about 4 percentage points
It is always more accurate
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What method is suggested to improve the approximation accuracy?
Using a larger sample size
Adjusting the mean
Using the midpoint in calculations
Increasing the variance
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the benefit of using the midpoint in the approximation method?
It increases the sample size
It simplifies the calculation
It provides a closer approximation to the true value
It decreases the variance
8.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How can individual binomial probabilities be approximated using the improved method?
By using the exact binomial formula
By considering the area under the normal PDF between specific points
By adjusting the variance
By increasing the sample size
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