Stat121 Lesson 9

Which of the following characterize a Normal distribution? A. Mean and standard deviation B. Mean and median C. Median and interquartile range D. Mean and interquartile range

(Mean and standard deviation) µ and σ characterize a Normal distribution.

What is the mean of the Standard Normal distribution?

0

What is the standard deviation of the Standard Normal distribution?

1

Approximately how many standard deviation distances are on either side of the mean?

3

What percentage of the area of a Normal curve lies within two standard deviations of the mean?

95%

What does a z-score tell us?

A z-score for an x-value tells us how many standard deviations the x-value is from the mean.

True or false: For density curves the height of the curve at a particular X-value equates to the proportion of values in the population that have that X value.

False. Area under the curve between two values estimates the proportion of the population in that interval.

True or false: The distance from the mean to the largest observation of a Normal distribution is equal to standard deviation.

False. Standard deviation equals the distance from the mean to the point where the curve begins to fall less steeply.

True or false: The symbol for the mean of a population, and for the mean of a sample, are the same.

False. μ denotes mean of population. x̅ denotes mean of a sample.

What is a density curve?

It is a mathematical curve invented to model the overall shape of the data so that probabilities can more easily be found.

What is standardizing?

Measuring in standard deviation units from the mean.

What is the name of the density curve that models many bell-shaped symmetric distributions?

Normal distribution.

Why do we model data with a density curve?

To estimate probabilities of various outcomes.

True or false: The area under the Standard Normal table gives the proportion of observations in that interval.

True

True or false: We use the table for the Standard Normal distribution to get areas for any Normal distribution.

True

True or false: the mean is the point of symmetry of a Normal distribution.

True

Which of the following is NOT a characteristic of a Normal distribution? A. Symmetric B. Two peaked C. Bell-shaped D. Mean equals median

b.

If the density curve is symmetric, then the mean is ____________ the median.

equal to

If the density curve is right-skewed, then the mean is __________ the median.

greater than. The mean is pulled towards the longest tail. So if the density curve is right-skewed, then the mean is to the right of the median.

If the density curve is left-skewed, then the mean is ____________ the median.

less than

Which measure of center represents the balance point of the density curve?

mean

Which measure of center is the point at which the area of the density curve is cut in half vertically?

median

What symbol represents the standard deviation of a sample?

s

What symbol represents the mean of a sample?

x̄

What symbol represents the mean of the density curve (population mean)?

μ

What symbol represents the density curve (population) standard deviation?

σ