Normal Distributions

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, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Tags

CCSS.HSS.ID.A.4

Front

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

Back

68%.

Tags

CCSS.HSS.ID.A.4

Front

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

Back

95%.

Tags

CCSS.HSS.ID.A.4

Front

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

Back

99.7%.

Tags

CCSS.HSS.ID.A.4

Front

If the mean is 75 and the standard deviation is 7, what percentage of scores are between 75 and 82?

Back

34%.

Tags

CCSS.HSS.ID.A.4

Front

If the mean is 38 and the standard deviation is 4, how many golfers are younger than 34 in a club of 500 members?

Back

80.

Tags

CCSS.HSF-LE.A.1B

Front

If the mean is 38 and the standard deviation is 4, what proportion of golfers are older than 42?

Back

16%.

Tags

CCSS.HSS.ID.A.4

Front

What is the formula for calculating the z-score?

Back

Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What does a z-score represent?

Back

A z-score represents the number of standard deviations a data point is from the mean.