Empirical Rule and Chebyshev

What is Chebyshev's Inequality?

• P≥1-1/(k²)
• P≥1+1/(k²)
• P≤1-1/(k²)
• P≤1+1/(k²)

What percent of the data in any data set lies within 7.5 standard deviations of the mean?

• 98.2%
• 86.7%
• 2.2%
• 13.3%

In any data set with 230 data points, what is the minimum number that must lie within 7 standard deviations of the mean?

• 226
• 40
• 204
• 153

In a data set with a mean of 24 and a standard deviation of 3, at least 75% of data points must lie between ________ and ________ [S.A.M.]

• 18 and 30
• 23.25 and 24.75
• 21 and 27
• 21.25 and 29.75

True or False: The percentages obtained by Chebyshev's Theorem are conservative lower estimates. The percent of data between any two boundaries is usually much more than the number given by the Theorem.

• True
• False

True or False: When finding the minimum number of data points between any two boundaries using Chebychev's Theorem, if a decimal is obtained, you should round that decimal to the nearest integer.

• True
• False

The set of the weights of professional football players was found to have a mean of 275 lbs. with a standard deviation of 15 lbs. If there are a total of 1,650 pro football players in the US, what is the minimum number that weigh between 250 and 300 lbs.?

• 1,056
• 1,603
• 952
• 879

The mean age of a dinosaur fossil in a particular fossil bed is 85 million years. The standard deviation of the fossil ages from this bed is 1.5 million years. At least __________ of fossils in this bed are between 80 and 90 million years old.

• 91%
• 76.7%
• 99.3%
• 70%

Scientists measured the area claimed by each Bengal tiger in a certain jungle. The mean area claimed was 30 square miles with s=2.8 mi². At least 99% of the areas in this sample would have to be between _________ and ________ mi² [S.A.M.]

• 2 and 58
• 27.2 and 32.8
• 20 and 40
• 17.2 and 42.8

What does the "k" in Chebyshev's Theorem represent?

• Standard deviation
• The number of standard deviations from the mean
• Variance
• The number of standard deviations from the median