Normal Distribution

Front

What is a Normal Distribution?

Back

A Normal Distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Front

What is the Empirical Rule?

Back

The Empirical Rule states that for a normal distribution: 68% of the data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.

Tags

CCSS.HSS.ID.A.4

Front

What percentage of data falls within 1 standard deviation in a normal distribution?

Back

68%

Tags

CCSS.HSS.ID.A.4

Front

What percentage of data falls within 2 standard deviations in a normal distribution?

Back

95%

Tags

CCSS.HSS.ID.A.4

Front

What percentage of data falls within 3 standard deviations in a normal distribution?

Back

99.7%

Tags

CCSS.HSS.ID.A.4

Front

If the average annual precipitation in Phoenix is 29 with a standard deviation of 3, what is the normal range (68%)?

Back

26-32

Tags

CCSS.HSS.ID.A.4

Front

What does it mean if data is normally distributed?

Back

It means that the data follows a bell-shaped curve where most of the observations cluster around the central peak and probabilities for values further away from the mean taper off equally in both directions.

Front

What is the significance of the mean in a normal distribution?

Back

The mean is the central value around which the data is distributed, and in a normal distribution, it is also the point of symmetry.

Tags

CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

Front

What is the significance of the standard deviation in a normal distribution?

Back

The standard deviation measures the dispersion or spread of the data points around the mean; a smaller standard deviation indicates that the data points are closer to the mean.

Front

How do you calculate the z-score?

Back

The z-score is calculated using the formula: z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.