Normal Distribution & Empirical Rule

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 data falls within 1 standard deviation of the mean, 95% falls within 2 standard deviations, and 99.7% falls within 3 standard deviations.

Front

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

Back

68%.

Front

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

Back

95%.

Front

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

Back

99.7%.

Front

If the mean age of golfers is 38 and the standard deviation is 4, what is the age range for approximately 95% of golfers?

Back

30 to 46 years old.

Front

In a normal distribution, if the mean is 12 days and the standard deviation is 3 days, what percentage of products last between 12 and 15 days?

Back

34%.

Front

How do you calculate the number of individuals below a certain value in a normal distribution?

Back

Use the mean and standard deviation to find the z-score, then refer to the standard normal distribution table.

Front

What is the z-score formula?

Back

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

Front

If a factory's concrete weight has a mean of 1150 pounds and a standard deviation of 22 pounds, what is the weight range for approximately 95% of molds?

Back

1106 to 1194 pounds.