Which of the following statements are TRUE about the Normal Distribution? Check all that apply.
a. The graph of the Normal Distribution is bell-shaped, with tapering tails that never actually touch the horizontal axis.
b. The distribution is symmetric with a single peak.
c. The mean, median and mode are all equal and occur at the center of the distribution.
d. About 95% of all data values lie within 1 standard deviation of the mean.
e. Data values are spread evenly around the mean.
f. 50% of the data values lie at or above the mean.
g. Data values farther from the mean are less common than data values closer to the mean.
All are true except D.
Hope this helps!
Google davidmlane normal distribution
Wow, it looks like you've got quite a list of statements there! Let me add some humor to this equation:
a. The statement about the graph being bell-shaped and the tails not touching the horizontal axis is TRUE. It's like a bell that's socially distanced from the axis!
b. The statement about the distribution being symmetric with a single peak is TRUE. It's as balanced as a seesaw with only one person on it!
c. The statement about the mean, median, and mode all being equal and occurring at the center is TRUE. That's the perfect recipe for some statistical harmony!
d. The statement about about 95% of data values lying within 1 standard deviation of the mean is TRUE. It's like having a safety net, just in case your data decides to wander off!
e. The statement about data values being spread evenly around the mean is FALSE. Sometimes, data values like to party and clump together in some areas more than others!
f. The statement about 50% of the data values lying at or above the mean is TRUE. It's like saying half of the people taking a test will get above the average, but that's assuming no one falls asleep on their keyboards!
g. The statement about data values farther from the mean being less common than data values closer to the mean is TRUE. It's like saying most people don't enjoy straying too far from the average, it's just too adventurous for them!
Remember, this is all in good fun, but I hope it helps clarify the true statements about the Normal Distribution for you!
To determine which statements are true about the Normal Distribution, we can use our knowledge about its characteristics.
a. The graph of the Normal Distribution is bell-shaped, with tapering tails that never actually touch the horizontal axis. - TRUE. The Normal Distribution is known for its bell-shaped curve that never touches the horizontal axis.
b. The distribution is symmetric with a single peak. - TRUE. The Normal Distribution is symmetric, meaning that the left and right halves of the curve are mirror images of each other. It also has a single peak at the mean.
c. The mean, median, and mode are all equal and occur at the center of the distribution. - TRUE. In the Normal Distribution, the mean, median, and mode are all equal and occur at the center of the distribution.
d. About 95% of all data values lie within 1 standard deviation of the mean. - TRUE. One of the properties of the Normal Distribution is that approximately 68% of values lie within one standard deviation of the mean, and about 95% of values lie within two standard deviations of the mean.
e. Data values are spread evenly around the mean. - FALSE. In the Normal Distribution, data values are not spread evenly around the mean. The spread of values depends on the standard deviation.
f. 50% of the data values lie at or above the mean. - TRUE. Since the Normal Distribution is symmetric, approximately 50% of the data values will lie at or above the mean, and 50% will lie below the mean.
g. Data values farther from the mean are less common than data values closer to the mean. - TRUE. The Normal Distribution is bell-shaped, meaning that data values farther from the mean are less common than those closer to the mean. This is why the tails of the distribution taper off gradually.
Therefore, the TRUE statements about the Normal Distribution are: a, b, c, d, and f.