The normal distribution and standard deviation

What is a normal distribution?

A symmetric, bell-shaped continuous probability distribution

In a normal distribution, how are the mean, median and mode related?

They are all equal

What does standard deviation measure?

The spread of values around the mean

What does a small standard deviation indicate?

Values are generally clustered close to the mean

How does a larger standard deviation affect the graph of a normal distribution?

It makes the curve wider and flatter

Approximately what percentage of observations in a normal distribution lie within one standard deviation of the mean?

68%

Approximately what percentage of observations in a normal distribution lie within two standard deviations of the mean?

95%

Approximately what percentage of observations in a normal distribution lie within three standard deviations of the mean?

99.7%

What is a standard normal distribution?

A normal distribution with mean 0 and standard deviation 1

What does a z-score represent?

The number of standard deviations a value is from the mean

Which formula gives the z-score of a value x when the mean is μ and the standard deviation is σ?

z = (x − μ) / σ

A value has a z-score of −2. What does this mean?

It is two standard deviations below the mean

What is represented by the total area under a normal distribution curve?

A probability of 1

A normal distribution has mean 50 and standard deviation 5. Which interval contains approximately 68% of its values?

45 to 55

If the same constant is added to every value in a data set, what happens to its standard deviation?

It remains unchanged

If every value in a data set is multiplied by 3, what happens to the standard deviation?

It is multiplied by 3

How are variance and standard deviation related?

Standard deviation is the square root of variance

Which statement about the tails of a normal distribution is correct?

They approach the horizontal axis but do not meet it