Understanding Sample Mean Distribution and Probabilities

This video tutorial demonstrates how to use Desmos.com to calculate probabilities and percentiles of a sample mean distribution. It covers the calculation of the mean and standard deviation for sample mean ages, explains the normal distribution of sample means, and shows how to find probabilities for specific age ranges. Additionally, it guides viewers through determining the 70th percentile for sample mean ages using Desmos.

What is the mean age of tablet users in the study?

• 25 years

• 30 years

• 35 years

• 40 years

How is the standard deviation of the sample mean ages calculated?

• Standard deviation of the population divided by the square root of the sample size

• Standard deviation of the population multiplied by the square root of the sample size

• Standard deviation of the population multiplied by the sample size

• Standard deviation of the population divided by the sample size

According to the central limit theorem, what does the distribution of sample means tend to?

• A normal distribution

• A skewed distribution

• A bimodal distribution

• A uniform distribution

What is the probability that the sample mean age is more than 27 years?

• Approximately 0.5

• Approximately 0.7

• Approximately 0.98

• Approximately 0.9

Which tool is used to graph the distribution of sample means?

• Desmos

• Excel

• Google Sheets

• MATLAB

What is the probability that the sample mean age is between 29 and 31 years?

• Approximately 0.52

• Approximately 0.35

• Approximately 0.75

• Approximately 0.25

What is the 70th percentile of the sample mean age?

• 29.5 years

• 30.0 years

• 30.7 years

• 31.5 years

What does the area under the curve to the left of the 70th percentile represent?

• 0.7

• 0.5

• 0.3

• 1.0

In the context of the video, what does the inverse CDF function help determine?

• The percentile of the sample mean

• The standard deviation of the sample

• The mode of the sample

• The mean of the sample

What percentage of sample mean ages are less than or equal to the 70th percentile?

• 60%

• 80%

• 50%

• 70%