Normal Distribution and the Empirical Rule (Topic 12)

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

Front

What does the mean represent in a normal distribution?

Back

The mean is the average of all data points in a distribution and is the center point of a normal distribution.

Front

What does the standard deviation indicate in a normal distribution?

Back

The standard deviation measures the amount of variation or dispersion of a set of values. A low standard deviation means that the values tend to be close to the mean, while a high standard deviation means that the values are spread out over a wider range.

Front

Calculate the interval for 95% of data in a normal distribution with a mean of 1150 and a standard deviation of 22.

Back

The interval is 1106 to 1194 pounds.

Front

If the mean age of golfers is 38 and the standard deviation is 4, what proportion of golfers are between 30 and 46 years old?

Back

Approximately 95% of golfers are between 30 and 46 years old.

Front

What is the probability of a soda can having less than 11.5 oz if the mean is 12 oz and the standard deviation is 0.25 oz?

Back

The probability is 2.5%.

Front

For a tire with a mean life of 30,000 km and a standard deviation of 2000 km, what is the range for 68% of tires?

Back

The range is 28,000 km to 32,000 km.

Front

What GPA corresponds to the highest 2.5% of students if the mean GPA is 2.9 and the standard deviation is 0.6?

Back

The GPA is 4.1 or higher.

Front

What is the z-score formula?

Back

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