The normal distribution and standard deviation

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

68%

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

It remains unchanged

How are variance and standard deviation related?

Standard deviation is the square root of variance

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

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

It makes the curve wider and flatter

What does a z-score represent?

The number of standard deviations a value is from the mean

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

It is two standard deviations below the mean

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

It is multiplied by 3

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

They approach the horizontal axis but do not meet it

What does standard deviation measure?

The spread of values around the mean

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

A probability of 1

What does a small standard deviation indicate?

Values are generally clustered close to 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 normal distribution has mean 50 and standard deviation 5. Which interval contains approximately 68% of its values?

45 to 55