Stats

Suppose that prices of recently sold homes in one neighborhood have a mean of $265,000$⁢265,000 with a standard deviation of $8600$⁢8600. Using Chebyshev's Theorem, state the range in which at least 88.9%88.9% of the data will reside. Please do not round your answers.

$239,200$⁢239,200 to $290,800

The empirical rule says that approximately 99.7%99.7% of data lies within 33 standard deviations of the mean. Because of the symmetry of the distribution, half of this 99.7%99.7% is above the mean and half is below. Thus, about 49.85%49.85% of the data is between the mean and 3.823.82. Also, since the bell-shaped distribution is symmetric, around 50%50% of the data is above the mean.

.15

Suppose that IQ scores have a bell-shaped distribution with a mean of 9696 and a standard deviation of 1717. Using the empirical rule, what percentage of IQ scores are less than 7979? Please do not round your answer.

16%

The empirical rule says that approximately 68%68% of data lies within 11 standard deviation of the mean. Because of the symmetry of the distribution, half of this 68%68% is above the mean and half is below. Thus, about 34%34% of the data is between 8686 and the mean. Also, since the bell-shaped distribution is symmetric, around 50%50% of the data is below the mean.

16%

The empirical rule says that approximately 95%95% of data lies within 22 standard deviations of the mean. Because of the symmetry of the distribution, half of this 95%95% is above the mean and half is below. Thus, about 47.5%47.5% of the data is between 6.41cm6.41⁢cm and the mean. Also, since the bell-shaped distribution is symmetric, around 50%50% of the data is below the mean.

2.5

Suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7.25cm7.25⁢cm and a standard deviation of 0.42cm0.42⁢cm. Using the empirical rule, what percentage of the apples have diameters that are no more than 6.41cm6.41⁢cm? Please do not round your answer.

2.5%

Suppose that quiz scores in a beginning statistics class have a mean of 7.47.4 with a standard deviation of 0.20.2. Using Chebyshev's Theorem, state the range in which at least 88.9%88.9% of the data will reside. Please do not round your answers.

6.86.8 to 8.0

Suppose that prices of recently sold homes in one neighborhood have a mean of $225,000$⁢225,000 with a standard deviation of $6900$⁢6900. Using Chebyshev's Theorem, what is the minimum percentage of recently sold homes with prices between $211,200$⁢211,200 and $238,800$⁢238,800? Round your answer to one decimal place.

75%

The empirical rule says that approximately 68%68% of data lies within 11 standard deviation of the mean. Because of the symmetry of the distribution, half of this 68%68% is above the mean and half is below. Thus, about 34%34% of the data is between the mean and 9494 mmHg. Also, since the bell-shaped distribution is symmetric, around 50%50% of the data is below the mean.

84

Suppose that quiz scores in a beginning statistics class have a mean of 6.46.4 with a standard deviation of 0.70.7. Using Chebyshev's Theorem, what is the minimum percentage of quiz scores between 4.34.3 and 8.58.5? Round your answer to one decimal place.

88.9%88.9%

The empirical rule says that approximately 95%95% of data lies within 22 standard deviations of the mean. Because of the symmetry of the distribution, half of this 95%95% is above the mean and half is below. Thus, about 47.5%47.5% of the data is between the mean and 133133. Also, since the bell-shaped distribution is symmetric, around 50%50% of the data is below the mean.

97.5