Understanding Probability and the Central Limit Theorem

This lesson covers using Desmos to determine probabilities of sums from a sample and finding a sum that is 1.5 standard deviations above the mean. It begins with a review of the central limit theorem for sums, explaining how sums form a normal distribution as sample size increases. The lesson then details calculating the mean and standard deviation of sums, followed by using Desmos to graph distributions and find probabilities. Finally, it demonstrates finding a sum that is 1.5 standard deviations above the mean.

What tool is introduced in the lesson for determining probabilities and sums?

• Python

• R Studio

• desmos.com

• Excel

According to the central limit theorem for sums, what happens as the sample size increases?

• The distribution approaches a normal distribution

• The distribution becomes skewed

• The standard deviation becomes zero

• The mean decreases

How is the mean of the sums calculated in the example?

• By dividing the original mean by the sample size

• By multiplying the original mean by the sample size

• By subtracting the sample size from the original mean

• By adding the original mean to the sample size

What is the standard deviation of the sums in the example?

• 12 times the square root of 50

• 50 times the square root of 12

• 12 divided by the square root of 50

• 50 divided by the square root of 12

Which website is used to graph the distribution of sums?

• Wolfram Alpha

• desmos.com

• Khan Academy

• Google Sheets

What is the probability that the sum of 50 values is less than 4350?

• 0.7500 or 75.00%

• 0.2778 or 27.78%

• 0.1000 or 10.00%

• 0.5000 or 50.00%

What is the probability that the sum is between 4300 and 4450?

• 0.7500 or 75.00%

• 0.6029 or 60.29%

• 0.5000 or 50.00%

• 0.2778 or 27.78%

How is the sum that is 1.5 standard deviations above the mean calculated?

• By adding 1.5 times the standard deviation to the mean

• By subtracting 1.5 times the standard deviation from the mean

• By multiplying the mean by 1.5

• By dividing the mean by 1.5

What is the approximate value of the sum that is 1.5 standard deviations above the mean?

• 4300

• 4450

• 4527.3

• 4400

What is the z-score used to find the sum that is above the mean?

• 1.0

• 1.5

• 2.0

• 2.5