Sampling Distributions and Central Limit Theorem

The video tutorial from EZ Academy introduces sampling distributions, explaining their definition and importance. It covers the rules of sampling distributions, including the mean and standard deviation, and discusses the correction factor and central limit theorem. The tutorial also demonstrates how to use the normal CDF function on a calculator to find probabilities. A practice problem is solved to reinforce the concepts learned, focusing on calculating probabilities for fish lengths in a pond using both population and sampling distribution parameters.

What is the average length of the fish population used in the sampling distribution example?

• 6 inches

• 5.5 inches

• 5 inches

• 4 inches

How is the mean of a sampling distribution related to the mean of the population?

• It is unrelated to the population mean.

• It is always less than the population mean.

• It is always greater than the population mean.

• It is equal to the population mean.

What is the formula for the standard deviation of a sampling distribution?

• Standard deviation of the population times the sample size

• Standard deviation of the population plus the sample size

• Standard deviation of the population divided by the sample size

• Standard deviation of the population over the square root of the sample size

When is a correction factor needed in calculating the standard deviation of a sampling distribution?

• When the sample size is less than 5% of the population

• When the sample size is more than 5% of the population

• When the sample size is irrelevant

• When the sample size is exactly 5% of the population

According to the third rule, when is a sampling distribution considered normal?

• When the population distribution is normal

• When the sample size is less than 10

• When the population distribution is skewed

• When the sample size is more than 100

What does the central limit theorem state about sampling distributions?

• They are normal only if the population is normal

• They are always uniform

• They are normal if the sample size is large enough

• They are always skewed

What function is used on a graphing calculator to find probabilities using normal distributions?

• normalPDF

• normalCDF

• binomialCDF

• poissonCDF

In the practice problem, what is the probability of selecting one fish with a length between 7.5 and 12.5 inches?

• 50%

• 85.10%

• 75%

• 59.53%

What is the mean length of fish used in the practice problem?

• 7.5 inches

• 10 inches

• 12.5 inches

• 15 inches

What assumption is made about the sample size in the practice problem?

• It is more than 5% of the population

• It is less than 5% of the population

• It is exactly 5% of the population

• It is irrelevant to the population size