Empirical Rule Quizlet

The sample mean speed of vehicles along a stretch of highway is 67 mi/h with a standard deviation of 4 mi/h.

Estimate the percentage, using the empirical rule, of vehicles whose speeds are between 63 mi/h and 71 mi/h.

68%

Empirical Rule

68%, 95%, 99.7%

The sample mean speed of vehicles along a stretch of highway is 67 mi/h with a standard deviation of 4 mi/h. The sample consisted of 75 vehicles.

Estimate, using the empirical rule, the number of vehicles whose speeds are between 63 mi/h and 71 mi/h.

51

Chebychev's Theorem

tells the portion of data that lies within k standard deviations of the mean

1 - 1/ k2 (k is squared)

The mean monthly utility bill for a sample of households in a city is $70 with a standard deviation of $8. Use the empirical rule to answer the following.

Between what two values does about 95% of the monthly bills lie?

$54-$86

The mean monthly utility bill for a sample of households in a city is $70 with a standard deviation of $8. Use the empirical rule to answer the following.

The sample contains 40 houses.

Estimate the number of households with bills between $54-$86.

38

The sample mean speed of vehicles along a stretch of highway is 67 mi/h with a standard deviation of 4 mi/h. Use the empirical rule to answer the following. Listed below are 8 speeds.

70, 78, 62, 71, 65, 76, 82, 64

Which speeds are unusual?

78. 76, and 82

The mean monthly utility bill for a sample of households in a city is $70 with a standard deviation of $8. Use empirical rule to answer the following. Listed below are 8 bill costs.

$65, $52, $63, $83, $77, $98, $84, $70

Which costs are unusual?

$52, and $98

The mean score on a European History exam is 88 points with a standard deviation of 4 points. Use Chebychev's Theorem to find the percent of scores that fall between 80-96 points.

75%

The mean time in the finals for the women's 800-meter freestyle at the 2012 Summer Olympics was 502.84 seconds with a standard deviation of 4.68. What percent of the times fall between 488.8 and 516.88, using Chebychev's Theorem?

88.9%

Which bell curve has 81.5% shaded?

Which bell curve has 83.85% shaded?

Which bell curve has 49.85% shaded?

How many standard deviations is 68% in the empirical rule?

1

How many standard deviations is 99.7% in the empirical rule?

3

When k=2, what does Chebychev's Theorem say about the data?

75% of it falls between 2 standard deviations

When k=3, what does Chebychev's Theorem say about the data?

88.9% of it falls between 3 standard deviations