Question 1

For every normal distribution, .9544 (95.44%) of the are under the curve lies between the mean and a point that is two standard deviations to the right and two standard deviations to the left of the mean

Accepted Answer

The Empirical Rule states that for a normal distribution, approximately 95% of the data falls within two standard deviations of the mean.

Question 2

In a normal distribution, a z-score of at least $\pm$ 1.96 is indicative of a rare event because it occurs 5% of the time or less

Accepted Answer

A z-score of $\pm$ 1.96 corresponds to the 95% confidence level in a normal distribution, meaning that scores beyond this range (in either direction) occur approximately 5% of the time, indicating a rare event.

Question 3

The larger a sample is the more imprecise the estimates are.

Accepted Answer

Larger samples tend to produce more precise estimates because they reduce the impact of random sampling error, leading to narrower confidence intervals and more reliable results.

Question 4

For every normal distribution, .9974 (99.74%) of the are under the curve lies between the mean and a point that is three standard deviations to the right and is three standard deviations to the left of the mean

Accepted Answer

In a normal distribution, approximately 99.74% of the data falls within three standard deviations of the mean, covering both directions from the mean.

Question 5

State and describe the three characteristics of the sampling distribution of the mean based on the Central Limit Theorem

Accepted Answer

The answer of State and describe the three characteristics of...

Quiz 6: Probability, Probability Distributions, and an Introduction to Inferential Statistics

For every normal distribution, .9544 (95.44%) of the are under the curve lies between the mean and a point that is two standard deviations to the right and two standard deviations to the left of the mean

In a normal distribution, a z-score of at least ±\pm± 1.96 is indicative of a rare event because it occurs 5% of the time or less

The larger a sample is the more imprecise the estimates are.

For every normal distribution, .9974 (99.74%) of the are under the curve lies between the mean and a point that is three standard deviations to the right and is three standard deviations to the left of the mean

State and describe the three characteristics of the sampling distribution of the mean based on the Central Limit Theorem

In a normal distribution, a z-score of at least $\pm$ 1.96 is indicative of a rare event because it occurs 5% of the time or less