Empirical Rule and Chevyshev

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, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

Front

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

Back

Approximately 68%.

Front

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

Back

Approximately 95%.

Front

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

Back

Approximately 99.7%.

Front

What is Chebyshev's Theorem?

Back

Chebyshev's Theorem states that for any distribution, at least (1 - 1/k²) of the data falls within k standard deviations of the mean, for k > 1.

Front

If k = 2 in Chebyshev's Theorem, what percentage of data falls within two standard deviations of the mean?

Back

At least 75%.

Front

If k = 3 in Chebyshev's Theorem, what percentage of data falls within three standard deviations of the mean?

Back

At least 88.89%.

Front

Given a mean of 30,000 km and a standard deviation of 2,000 km, what is the range for 68% of tires?

Back

28,000 km to 32,000 km.

Front

In a normal distribution, if the mean is 1150 pounds and the standard deviation is 22 pounds, what is the weight range for 95% of molds?

Back

1106 pounds to 1194 pounds.

Front

What is the formula to calculate the range for a given percentage using the Empirical Rule?

Back

Mean ± (Z-score * Standard Deviation), where Z-score corresponds to the percentage.