Question 1

The annual incomes of all MBA degree holders working in Los Angeles have a bell-shaped distribution with a mean of $72,000 and a standard deviation of $6,000.According to the empirical rule,the percentage of MBA degree holders working in Los Angeles who have an annual income of $54,000 to $90,000 is approximately:

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Question 2

The empirical rule is applicable to:

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...

Question 3

The ages of all high school teachers in New York state have a bell-shaped distribution with a mean of 39 years and a standard deviation of 7 years.According to the empirical rule,the percentage of teachers in this state who are 32 to 46 years old is approximately:

Accepted Answer

According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean in a bell-shaped distribution. Here, 32 to 46 years is within one standard deviation (39 ± 7).

Question 4

The ages of all high school teachers in New York state have a bell-shaped distribution with a mean of 43 years and a standard deviation of 6 years.According to the empirical rule,the percentage of teachers in this state who are 31 to 55 years old is approximately:

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Question 5

According to the empirical rule,the percentage of values that fall within two standard deviations of the mean is approximately:

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Question 6

According to the empirical rule,the percentage of values that fall within three standard deviations of the mean is approximately:

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Question 7

The mean income of all MBA degree holders working in Los Angeles is $65,000 per year and the standard deviation of their incomes is $8,000 per year.According to Chebyshev's theorem,the percentage of MBA degree holders,working in Los Angeles,with an annual income of $33,000 to $97,000 is at least:

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Question 8

Chebyshev's theorem is applicable to:

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The answer of Chebyshev's theorem is applicable to:
...

Question 9

According to Chebyshev's theorem,the minimum percentage of values that fall within 3 standard deviations of the mean is:

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Question 10

According to the empirical rule,the percentage of values that fall within one standard deviation of the mean is approximately:

Accepted Answer

The empirical rule states that approximately 68% of data in a normal distribution falls within one standard deviation of the mean.

Question 11

The mean age of all high school teachers in New York state is 41 years and the standard deviation is 6 years.According to Chebyshev's theorem,the percentage of teachers in New York who are 23 to 59 years old is at least:

Accepted Answer

Chebyshev's theorem states that at least (1 - 1/k^2) of the data falls within k standard deviations of the mean. Here, 23 to 59 years is 3 standard deviations from the mean (41 ± 3*6). So, at least (1 - 1/3^2) = 88.89% of the data falls within this range.

Question 12

The annual incomes of all MBA degree holders working in Los Angeles have a bell-shaped distribution with a mean of $71,000 and a standard deviation of $8,000.According to the empirical rule,the percentage of MBA degree holders working in Los Angeles who have an annual income of $63,000 to $79,000 is approximately:

Accepted Answer

According to the empirical rule, approximately 68% of data falls within one standard deviation of the mean in a bell-shaped distribution. $63,000 to $79,000 is within one standard deviation ($71,000 ± $8,000).

Question 13

The mean income of all MBA degree holders working in Los Angeles is $86,000 per year and the standard deviation of their incomes is $10,500 per year.According to Chebyshev's theorem,the percentage of MBA degree holders,working in Los Angeles,with an annual income of $49,250 to $122,750 is at least::

Accepted Answer

Chebyshev's theorem states that at least (1 - 1/k^2) of the data falls within k standard deviations of the mean. Here, k = (122,750 - 86,000) / 10,500 = 3.5. So, at least (1 - 1/3.5^2) = 91.84% of incomes fall within this range.

Question 14

The annual incomes of all MBA degree holders working in Los Angeles have a bell-shaped distribution with a mean of $78,000 and a standard deviation of $11,000.According to the empirical rule,the percentage of MBA degree holders working in Los Angeles who have an annual income of $56,000 to $100,000 is approximately:

Accepted Answer

According to the empirical rule, approximately 95% of the data falls within two standard deviations of the mean in a bell-shaped distribution. $56,000 and $100,000 are two standard deviations below and above the mean, respectively.

Question 15

Use the following to answer questions :
The following table gives the frequency distribution of prices for a sample of 30 college textbooks.
 
-The variance of the textbook prices,rounded to two decimal places,is:

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The answer of Use the following to answer questions :
The...

Question 16

The mean age of all high school teachers in New York state is 50 years and the standard deviation is 7 years.According to Chebyshev's theorem,the percentage of teachers in New York who are 25.5 to 74.5 years old is at least:

Accepted Answer

Chebyshev's theorem states that at least (1 - 1/k^2) of the data lies within k standard deviations of the mean. Here, k = (74.5 - 50) / 7 = 3.5. So, at least (1 - 1/3.5^2) = 91.84% of the data lies within this range.

Question 17

According to Chebyshev's theorem,the minimum percentage of values that fall within 1.5 standard deviations of the mean is:

Accepted Answer

Chebyshev's theorem states that at least (1 - 1/k^2) of data values fall within k standard deviations of the mean. For k = 1.5, this is (1 - 1/1.5^2) = 55.56%.

Question 18

The ages of all high school teachers in New York state have a bell-shaped distribution with a mean of 45 years and a standard deviation of 7 years.According to the empirical rule,the percentage of teachers in this state who are 24 to 66 years old is approximately:

Accepted Answer

According to the empirical rule, approximately 99.7% of data in a bell-shaped distribution falls within three standard deviations of the mean. Here, 24 to 66 years is within three standard deviations (21 years) from the mean (45 years).

Question 19

According to the empirical rule,the percentage of values that fall outside two standard deviations of the mean is approximately:

Accepted Answer

According to the empirical rule, approximately 95% of data falls within two standard deviations of the mean, leaving about 5% outside this range.

Question 20

Use the following to answer questions :
The following table gives the frequency distribution of prices for a sample of 30 college textbooks.
 
-The standard deviation of the textbook prices,rounded to two decimal places,is:

Accepted Answer