Understanding Sample Means and Probabilities

The video tutorial demonstrates how to use the TI-84 calculator to determine probabilities of sample means from a population with a known mean and standard deviation. It explains the central limit theorem, showing that the distribution of sample means is normal. The tutorial guides through calculating probabilities for sample means within specific ranges and beyond certain values using the normal cdf function on the TI-84. It also covers finding a value two standard deviations above the mean of the sample distribution.

What is the mean of the unknown distribution in the given problem?

• 85

• 90

• 92

• 95

According to the Central Limit Theorem, what is the distribution of sample means?

• Poisson

• Normal

• Exponential

• Uniform

How is the standard deviation of the sample means calculated?

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

• Standard deviation of population multiplied by sample size

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

• Standard deviation of population divided by sample size

Which function on the TI-84 is used to find the probability of a sample mean being between two values?

• invNorm

• normalcdf

• binomcdf

• normalpdf

What is the probability that the sample mean is between 85 and 92?

• 25.25%

• 69.97%

• 50%

• 4.78%

What is the exaggerated upper bound used for calculating the probability that the sample mean is greater than 92?

• 10000

• 99999

• 100000

• 9999

What is the probability that the sample mean is greater than 92?

• 25.25%

• 4.78%

• 50%

• 69.97%

What is the exaggerated lower bound used for calculating the probability that the sample mean is less than 85?

• -9999

• -100000

• -99999

• -10000

What is the probability that the sample mean is less than 85?

• 4.78%

• 50%

• 69.97%

• 25.25%

What is the value that is two standard deviations above the expected value of the sample mean?

• 99

• 93

• 90

• 96