When is a large population said to have a normal distribution?

When the frequencies of observations produce a histogram that follows the pattern of a smooth bell-shaped curve

Describe the spread of a normal distribution

It is symmetric about the population mean μ

How is a normal distribution distributed?

X~N(μ, σ^{2})

What does the negative tail of a normal distribution extend to?

-∞

What does the positive tail of a normal distribution extend to?

+∞

What percentage of values fall within 1 standard deviation above or below the mean?

68%

What percentage of values fall within 2 standard deviations above or below the mean?

95%

What percentage of values fall within 3 standard deviations above or below the mean?

99.7%

What are probabilities (proportions) in terms of a normal distribution?

Areas under a normal curve

Describe the n^{th} percentile of a data set

The smallest value in a set with the probability that n% of values are less than or equal to it

What percentile is a data value that lies between two percentiles said to lie in?

The lower percentile

How is a standard normal curve distributed?

X~N(0,1)

How can Z be calculated?

*Z=(x-*μ)*/* σ

What are the 6 required steps for calculating normal probabilities?

1. Define the variable of interest

2. Form a probability statement

3. Convert to a z‐score if necessary

4. Draw a picture and shade the required area

5. Find the probability you need using the Standard Normal Table

6. Comment on the results

How do you convert a Z-Score to a raw score (x)?

Using x=μ+Z(σ)

What is the Z-Score of a measurement defined as?

The number of standard deviations the measurement is away from the mean

What two things can Z-Scores be used to do?

Compare values from different data sets

Identify unusual values

What are unusual values in terms of Z-Scores?

Z2

What are two ways to verify data is normally distributed?

Look at the bell curve

Determine if the 1st, 2nd, and 3rd distributions contain 68, 95 and 99.7% of the data

What is the sampling distribution of a statistic?

The distribution of values taken by the statistic in all possible samples of the same size from the same population

What is the formula of sample standard deviation of a sampling distribution?

σ/√n

What does the central limit theorem state?

The approximation becomes more and more accurate as the sample size n is increased.

Are means of random samples more or less variable than individual observations?

Less variable

Are means of random samples more or less normal than individual observations?

More normal

What is the Z-Score calculation for a sample mean?

Z=x̄-μ_{x̄}/(σ/√n)

If the original population is not normally distributed, what criteria must be satisfied for the CLT to hold?

The sample size, n must be at least 30.

If the parent distribution is normal, when is the distribution of the sample mean said to be normal?

If the parent distribution is normal, the distribution of the sample mean is normal regardless of sample size n.