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nature of mathematics

Questions and Answers of Nature Of Mathematics

In Problems 23-30, find the range and the standard deviation (correct to two decimal places). If you do not have a calculator, find the range and the variance.\(0,1,1,2,3,4,16,21\)
By looking at Problems \(11-14\) and 23-26 and discovering a pattern, answer the following questions about the numbers \(217,849,217,850,217,851,217,852\), and 217,853 .a. What is the mean?b. What is
In 2010 Andy's batting average was better than Dave's; and in 2011 Andy once again beat Dave. Does it follow that Andy's combined 2010-2011 batting average is better than Dave's? Andy AB Hits 2010
Find the mean, the median, and the mode of the following salaries of employees of the Moe D. Lawn Landscaping Company: Salary $25,000 28,000 30,000 45,000 Frequency 4 3 2 1
G. Thumb, the leading salesperson for the Moe D. Lawn Landscaping Company, turned in the following summary of sales for the week of October 23-28:Find the mean, median, and mode. Date Oct. 23 Oct. 24
Find the mean, the median, and the mode of the following scores: Test Score 90 80 70 60 50 Frequency 1 3 9 NS6 5 2
A class obtained the following scores on a test:Find the mean, the median, the mode, and the range for the class. Test Score 90 80 70 60 50 40 Frequency 1 6 10 4 3 1
A class obtained the following test scores:Find the mean, median, mode, and range for the class. Test Score 90 80 70 60 50 40 30 0 Frequency 2 4 9 5 3 1 2 4
The county fair reported the following total attendance (in thousands).Find the mean, median, and mode for the attendance figures (rounded to the nearest thousand). Year Attendance 2012 2011 2010
The following chart shows the most popular choices for a girl's name. In a certain group, each person was asked to vote for one name, and the results are shown.Find the mean, the median, and the mode
The sale prices for homes in a certain city are as follows:Find the mean, the median, and the mode. Which measure seems to best describe the home price? Location 415 First Street 957 Locust Street
The graph in Figure 14.32 shows the distribution of scores on an examination.Figure 14.32Which of the following statements is true about the distribution?A. The mean is less than the mode.B. The
The graph in Figure 14.33 shows the salaries of the employees for a certain company.Figure 14.33Which of the following statements is true about the distribution?A. The mean is less than the mode.B.
Shoe size for a team of football players ranges from size 10 to 14 . The majority of players wear size 12 , and the number of players wearing size 11 is the same as the number wearing size 13.It is
In a survey, members of a math class were asked how many minutes per week they exercised. There were three possible responses: 10 minutes or less ( \(70 \%\) checked this), between 10 and 60 minutes
Use the nutritional information about candy bars given in Table 14.7 to answer the questions in Problems 45 and 46.Table 14.7a. What is the mean calories from fat?b. What is the median (in grams) of
Use the nutritional information about candy bars given in Table 14.7 to answer the questions in Problems 45 and 46.Table 14.7a. Find the three quartiles for serving size.b. Draw a box plot for the
Find the standard deviation (rounded to the nearest unit) for the data indicated in Problems 47-52.Data from Problem 33 Salary $25,000 28,000 30,000 45,000 Frequency 4 3 2 1
Find the standard deviation (rounded to the nearest unit) for the data indicated in Problems 47-52.Data from Problem 34 Date Oct. 23 Oct. 24 Oct. 25 Oct. 26 Oct. 27 Oct. 28 No. of Clients 12 9 10 16
Find the standard deviation (rounded to the nearest unit) for the data indicated in Problems 47-52.Data from Problem 35 Test Score 90 80 70 60 50 Frequency 1 3 9 95 5 2
Find the standard deviation (rounded to the nearest unit) for the data indicated in Problems 47-52.Data from Problem 36 Test Score 90 80 70 60 50 40 Frequency 1 6 10 4 3 1
Find the standard deviation (rounded to the nearest unit) for the data indicated in Problems 47-52.Data from Problem 37 Test Score 90 80 70 60 50 40 30 0 Frequency 2 4 9 5 3 1 2 4
Find the standard deviation (rounded to the nearest unit) for the data indicated in Problems 47-52.Data from Problem 38 Year Attendance 2012 2011 2010 2009 2008 2007 366 391 358 373 346 364
The number of miles driven on each of five tires was 17,000 , \(19,000,19,000,20,000\), and 21,000. Find the mean, the range, and the standard deviation (rounded to the nearest unit) for these
Roll a pair of dice 20 times and record the frequency of each outcome. Find the mean, the median, the mode, and the range of the number of tosses.
Roll a pair of dice until all 11 possible sums occur at least once. Repeat the experiment 10 times. Find the mean, the median, the mode, and the range of the number of tosses.
When you take the Scholastic Assessment Test (SAT), your score is recorded as a percentile score. If you scored in the 92nd percentile, it means that you scored better than approximately \(92 \%\) of
The mean defined in the text is sometimes called the arithmetic mean to distinguish it from other possible means. For example, a different mean, called the harmonic mean (H.M.), is used to find
The mean defined in the text is sometimes called the arithmetic mean to distinguish it from other possible means. For example, a different mean, called the geometric mean (G.M.), is used in business
The example about averages of bowling scores at the beginning of this section is an instance of what is known as Simpson's paradox. The following example illustrates this paradox.Notice that Player A
Let \(Q_{1}, Q_{2}\), and \(Q_{3}\) be the quartiles for a large population of scores. Is the following always, sometimes, or never true (explain your reasoning)?\[Q_{2}-Q_{1}=Q_{3}-Q_{2}\]
What do we mean by a cumulative frequency?
What does it mean to "grade on a curve"?
What is a normal curve?
What does the \(z\)-score, or standard score, represent?
Find the cumulative distribution, the mean, median, and mode for each of the tables in Problems 5-10.The number of bedrooms of homes in a certain community is shown in the table below. Number of
Find the cumulative distribution, the mean, median, and mode for each of the tables in Problems 5-10.The cumulative grade point average of graduating seniors at a small liberal arts college is shown
Find the cumulative distribution, the mean, median, and mode for each of the tables in Problems 5-10.The table gives the distribution of the number of exemptions claimed by employees of a large
Find the cumulative distribution, the mean, median, and mode for each of the tables in Problems 5-10.The table shows the distribution of the number of motor vehicles per household. No. of Motor
Find the cumulative distribution, the mean, median, and mode for each of the tables in Problems 5-10.A store orders tubes of glue in the proportions shown in the following table. Size (oz) 2 268 6 8
Find the cumulative distribution, the mean, median, and mode for each of the tables in Problems 5-10.The distribution of number of years of education of employees of a large company is shown in the
What percent of the total population is found between the mean and the z-score given in Problems 11-22?\(z=1.4 \)
What percent of the total population is found between the mean and the z-score given in Problems 11-22?\(z=0.3 \)
What percent of the total population is found between the mean and the z-score given in Problems 11-22?\(z=2.43 \)
What percent of the total population is found between the mean and the z-score given in Problems 11-22?\(z=1.86 \)
What percent of the total population is found between the mean and the z-score given in Problems 11-22?\(z=3.25\)
What percent of the total population is found between the mean and the z-score given in Problems 11-22?\(z=-0.6 \)
What percent of the total population is found between the mean and the z-score given in Problems 11-22?\(z=-2.33 \)
What percent of the total population is found between the mean and the z-score given in Problems 11-22?\(z=-0.50 \)
What percent of the total population is found between the mean and the z-score given in Problems 11-22?\(z=-0.46 \)
What percent of the total population is found between the mean and the z-score given in Problems 11-22?\(z=-1.19 \)
What percent of the total population is found between the mean and the z-score given in Problems 11-22?\(z=-2.22 \)
What percent of the total population is found between the mean and the z-score given in Problems 11-22?\(z=-3.41\)
In Problems 23-26, suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 50 people.a. How many would you
In Problems 23-26, suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 50 people.a. How many would you
In Problems 23-26, suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 50 people.What is the variance in
In Problems 23-26, suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 50 people.What is the cumulative
In Problems 27-30 suppose that, for a certain exam, a teacher grades on a curve. It is known that the mean is 50 and the standard deviation is 5.There are 45 students in the class.a. How many
In Problems 27-30 suppose that, for a certain exam, a teacher grades on a curve. It is known that the mean is 50 and the standard deviation is 5.There are 45 students in the class.a. What score would
In Problems 27-30 suppose that, for a certain exam, a teacher grades on a curve. It is known that the mean is 50 and the standard deviation is 5. There are 45 students in the class.What is the
In Problems 27-30 suppose that, for a certain exam, a teacher grades on a curve. It is known that the mean is 50 and the standard deviation is 5. There are 45 students in the class.What is the
Identify each distribution in Problems 31-34 as skewed to the right, symmetric, or skewed to the left. If it is also a normal distribution, so state. a. b. 600 450 300 150 0 600 450 300 150 0 Mode 0
Identify each distribution in Problems 31-34 as skewed to the right, symmetric, or skewed to the left. If it is also a normal distribution, so state. a. b. 600 450 300 150 0 600 450 300 150 0 Mode
Identify each distribution in Problems 31-34 as skewed to the right, symmetric, or skewed to the left. If it is also a normal distribution, so state. a. 600 450 300 150 0 Modes 0 1 2 3 4 Median = 4 5
Identify each distribution in Problems 31-34 as skewed to the right, symmetric, or skewed to the left. If it is also a normal distribution, so state. a. b. 600 450 300 150 0 600 450 300 150 012 3
In Problems 35-39, suppose that, for a certain mathematics class, the scores are normally distributed with a mean of 75 and a standard deviation of 8. The teacher wishes to give A's to the top \(6
In Problems 35-39, suppose that, for a certain mathematics class, the scores are normally distributed with a mean of 75 and a standard deviation of 8. The teacher wishes to give A's to the top \(6
In Problems 35-39, suppose that, for a certain mathematics class, the scores are normally distributed with a mean of 75 and a standard deviation of 8. The teacher wishes to give A's to the top \(6
In Problems 35-39, suppose that, for a certain mathematics class, the scores are normally distributed with a mean of 75 and a standard deviation of 8. The teacher wishes to give A's to the top \(6
What is the cumulative distribution?
In a distribution that is skewed to the right, which has the greatest value-the mean, median, or mode? Explain why this is the case.
In a distribution that is skewed to the left, which has the greatest value-the mean, median, or mode? Explain why this is the case.
A normal distribution has a mean of 85.7 and a standard deviation of 4.85. Find data values corresponding to the values of z given in Problems 42-45.\(z=0.85 \)
A normal distribution has a mean of 85.7 and a standard deviation of 4.85. Find data values corresponding to the values of z given in Problems 42-45.\(z=2.55 \)
A normal distribution has a mean of 85.7 and a standard deviation of 4.85. Find data values corresponding to the values of z given in Problems 42-45.\(z=-1.25 \)
A normal distribution has a mean of 85.7 and a standard deviation of 4.85. Find data values corresponding to the values of z given in Problems 42-45.\(z=-3.46\)
Suppose that the breaking strength of a rope (in pounds) is normally distributed, with a mean of 100 pounds and a standard deviation of 16 . What is the probability that a certain rope will break
The diameter of an electric cable is normally distributed, with a mean of 0.9 inch and a standard deviation of 0.01 inch. What is the probability that the diameter will exceed 0.91 inch?
Suppose that the annual rainfall in Ferndale, California, is known to be normally distributed, with a mean of 35.5 inches and a standard deviation of 2.5 inches. About \(2.3 \%\) of the years, the
About what percent of the years will it rain more than 36 inches in Ferndale (see Problem 48)?Data from Problem 48Suppose that the annual rainfall in Ferndale, California, is known to be normally
In Problem 48, what is the probability that the rainfall in a given year will exceed 30.5 inches in Ferndale?Data from Problem 48Suppose that the annual rainfall in Ferndale, California, is known to
The breaking strength (in pounds) of a certain new synthetic is normally distributed, with a mean of 165 and a variance of 9.The material is considered defective if the breaking strength is less than
The diameter of a pipe is normally distributed, with a mean of 0.4 inch and a variance of 0.0004 . What is the probability that the diameter of a randomly selected pipe will exceed 0.44 inch?
The diameter of a pipe is normally distributed, with a mean of 0.4 inch and a variance of 0.0004 . What is the probability that the diameter of a randomly selected pipe will exceed 0.41 inch?
Suppose the neck size of men is normally distributed, with a mean of 15.5 inches and a standard deviation of 0.5 inch. A shirt manufacturer is going to introduce a new line of shirts. Assume that if
A package of Toys Galore Cereal is marked "Net Wt. 12 oz." The actual weight is normally distributed, with a mean of 12 \(\mathrm{oz}\) and a variance of 0.04 .a. What percent of the packages will
Instant Dinner comes in packages with weights that are normally distributed, with a standard deviation of \(0.3 \mathrm{oz}\). If \(2.3 \%\) of the dinners weigh more than \(13.5 \mathrm{oz}\), what
JOURNAL PROBLEM The graph shown in Figure 14.42 is from the February 1991 issue of Scientific American. If the curve in the middle is a standard normal curve, describe the variance of the upper curve
The equation for the standard normal curve is an exponential equation:\[y=\frac{e^{-x^{2} / 2}}{\sqrt{2 \pi}}\]Evaluate this formula for\[x=-4,-3, \cdots, 3,4 . \quad \text {}\]
Calculate values for the equation \(y=2^{-x^{2}}\) and compare with the standard normal curve in Problem 58.List some similarities and some differences.Data from Problem 58The equation for the
The equation for a general normal curve with mean \(\mu\) and standard deviation \(\sigma\) is \[y=\frac{e^{-(x-\mu)^{2} /\left(2 \sigma^{2}ight)}}{\sigma \sqrt{2 \pi}}\]Calculate values \(x=20,30,
What do we mean by correlation?
What is a least squares line?
How do you find a linear correlation coefficient? See above.
How do you determine whether there is a linear correlation between two variables \(x\) and \(y\) ? Use Table 14.10.Table 14.10 n a = 0.05 0.950 0.878 4 5 6 0.811 7 0.754 8 0.707 9 0.666 10 0.632 11
Discuss the correlation shown by the following chart. Age-adjusted deaths per 100,000 population 30 25 20 15 10 0 5 Philippines. 0 Thailand 20 South Africa Venezuela Chile Panama Colombia Japan 40
Discuss the correlation shown by the following chart. Relative stride length 7 6 5 4 M Various quadrupeds (cat to rhinoceros) Human (biped) Kangaroo (biped) 2 5 10 Froude Number gl 15 20
In Problems 7-18, a sample of paired data gives a linear correlation coefficient \(r\). In each case, use Table 14.10 to determine whether there is a significant linear
In Problems 7-18, a sample of paired data gives a linear correlation coefficient \(r\). In each case, use Table 14.10 to determine whether there is a significant linear
In Problems 7-18, a sample of paired data gives a linear correlation coefficient \(r\). In each case, use Table 14.10 to determine whether there is a significant linear

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