Math - Combination for Final

According to a news​ publication, the following are five popular​ "maintenance" activities performed as summer​ approaches; 1 Prep the car for road​ trips; 2 Clean up the house or​ apartment; 3 Groom the​ garden; 4 Exercise the​ body; 5 Organize the wardrobe. The following data are the responses of 30 people who were​ asked, on June​ 1st, how many of the five they had accomplished. Complete parts​ (a) through​ (c) below.

(a) Construct frequency and relative frequency distributions. Number x Frequency f Relative Frequency StartFraction f Over n EndFraction 0 9 30​% 17 23​% 2 5 17​% 3 5 17​% ​(Round to the nearest integer as​ needed.) 4 13​%​(Round to the nearest integer as​ needed.) 5 3 10​%​(Round to the nearest integer as​ needed.) ​(b) Construct a histogram. Choose the correct graph below.

For the following list of​ data, calculate ​(a) the​ mean, ​(b) the​ median, and ​(c) the mode or modes​ (if any). 1.8​,5,6.3​,8,8​,4.8​,2.8​,4.8

(a) The mean is 5.2. ​(Round to the nearest tenth as​ needed.) ​(b) The median is 4.9. ​(c) Select the correct choice below and fill in any answer boxes within your choice. Mode

The accompanying table includes only countries in the top ten in a certain year for both production and consumption of energy.​ (Energy units are quadrillion​ Btu.) Population is for midyear of a certain​ year, in millions. The given box plot shows population in million people. Complete parts​ (a) through​ (c) below.

(a) What does the box plot for population indicate about the central tendency of the population ​data? The median is 250 million people.​(Type an integer or a decimal. Round to the nearest ten as​ needed.) ​(b) What does the box plot for population indicate about the dispersion of the population ​data?The range is 1330million people ​(Type an integer or a decimal. Round to the nearest ten as​ needed.) ​(c) What does the box plot for population indicate about the location of the middle half of the data items of the population ​data? The middle half of the data items extend from 150 to 1200 million people

Elizabeth and Angela skate for their college​ speed-skating team. In the last​ race, Elizabeth skated the 500 dash meter race in 59seconds. The average for this race is 65 seconds with a standard deviation of 4.0 seconds. Angela skated the​ 1000-meter race in 135 seconds. The average for this race is 140 seconds with a standard deviation of 10.0 seconds. Find the z dash score for each skater. Relatively​ speaking, which skater had the faster​ time?

-1.5, -0.5 Elizabeth

The mean clotting time of blood is 7.35​ seconds, with a standard deviation of 0.35 seconds. The times are approximately normally distributed. What is the probability that a randomly selected blood clotting time will be less than 7​ seconds? Round your answer to three decimal places as needed. A. 0.363 B. 0.156 C. 0.841 D. 0.159 This is the correct answer.

0.159

outlier 12.2

1) A piece of data that is quite separated from the rest of the data 2) should usually be considered as possible errors in the data 3) A value much greater or much less than the others in a data set

weighting factor 12.2

1) the number of units in 2) a mathematical factor used to make a disproportionate sample representative.

incorrect, 12.3-7 Find the standard deviation. Round to one more place than the data. Start 6 By 2 Table 1st Row 1st Column Age left parenthesis yr right parenthesis 2nd Column Frequency 2nd Row 1st Column 14 2nd Column 30 3rd Row 1st Column 15 2nd Column 25 4st Row 1st Column 16 2nd Column 42 5st Row 1st Column 17 2nd Column 33 6st Row 1st Column 18 2nd Column 47 EndTable

1.4

class width

12.1 1) for the distribution is the difference of any two successive lower class limits 2) or of any two successive upper class limits

descriptive statistics

12.1 collecting, organizing, summarizing, & presenting data (information)

inferential statistics

12.1 drawing inferences or conclusions (making conjectures) about populations on the basis of information from samples

raw data

12.1 information that has been collected but not yet organized of processed

sample

12.1 some but ordinarily not all, of the items in population

expected frequency distribution

12.1 the 1st 2 columns of table

upper class limits

12.1 the largest unit in a class of class (10-19) upper class limit is 19

observed (empirical) frequencies

12.1 the results from the 1st 2 columns

lower class limits

12.1 the smallest possible data values within the respective classes of class (10-19) lower class limit is 10

expected (theoretical) frequencies

12.1 uses binomial probability formula

grouped frequency distribution

12.1 1. Make sure each data item will fit into one, and only one, class. 2. Try to make all classes the same width. 3. Make sure the classes do not overlap. 4. Use from 5 to 12 classes. Too few or too many classes can obscure the tendencies in the data.

bar graph

12.1 A frequency distribution of non-numerical observations

population

12.1 all items of interest; * includes sample *

line graph

12.1 demonstrates how a quantity changes >> use a line to connect points

circle graph (pie chart)

12.1 graphic alternative to the bar graph

histogram

12.1 a series of rectangles whose lengths represent the frequencies and placed next to one another

stem-and-leaf display

12.1 a tool of exploratory data analysis

classes

12.1 data sets

class mark

12.1 middle value

frequency distribution

12.1 organized data set that includes many repeated items 1) distinct data value (x) 2) with their frequencies (f)

qualitative (non-numerical) data

12.1 page 645

quantitative (numerical) data

12.1 page 645

ranked data

12.1 quantitative data arranged in numerical order

frequency polygon classes

12.1 simple plot a single point at the appropriate height for each frequency, connect the point with a series of connected & complete the polygon with segments that trail down to the axis

relative frequency distribution

12.1 the fraction, or % of data set represented by the item 1) If n denotes the total number of items, and a given item, x, occurred f times, then the relative frequency of x is f/n.

measure of central tendency

12.2 the middle value of the set

At one high​ school, the mean time for running the​ 100-yard dash is 15.2 seconds with a standard deviation of 0.9 seconds. The times are very closely approximated by a normal curve. Find the percent of times that are between 16.1 and 17 seconds. Round your answer to the nearest tenth of a percent. A. ​12.4% B. ​34.7% C. ​13.6% This is the correct answer. D. ​27.6%

13.6%

SPA Corporation has about​ 23,500 employees who serve as security guards. The average length of service for these employees is 9.3 years with a standard deviation of 4.2 years. Compute the length of service for each employee. Round to the nearest​ one-tenth of a year. Upper A time in service with a z​-score of 1.3 A time in service with a​ z-score of minus 0.5

1438, 7.2

The graph shows government receipts and outlays​ (both on-budget and​ off-budget) for 1991 minus 2001 In what years did receipts appear to climb faster than​ outlays?

1995,1996,1997,2001

Find the standard deviation. Round to the nearest tenth as needed. 86​,23​,76​,37​,31​,61​,64​,57​,21

23.5

A company installs​ 5,000 light bulbs. The lifetimes of the lightbulbs are approximately normally distributed with a mean of 500 hours and a standard deviation of 100 hours. Find the approximate number of bulbs that can be expected to last between 290 hours and 500 hours.

2410

A company installs​ 5,000 light bulbs. The lifetimes of the lightbulbs are approximately normally distributed with a mean of 500 hours and a standard deviation of 100 hours. Find the approximate number of bulbs that can be expected to last less than 500 hours.

2500

Find the percent of the total area under the curve between z=0.54 and z=1.91. Round your answer to the nearest tenth of a percent.

26.7%

Find the mean for the given frequency distribution. Round your answer to the nearest tenth as needed. Start 6 By 2 Table 1st Row 1st Column Value 2nd Column Frequency 2nd Row 1st Column 136 2nd Column 1 3rd Row 1st Column 186 2nd Column 3 4st Row 1st Column 233 2nd Column 3 5st Row 1st Column 312 2nd Column 4 6st Row 1st Column 368 2nd Column 3 EndTable

267.5

Find the median for the given frequency distribution. Start 6 By 2 Table 1st Row 1st Column Value 2nd Column Frequency 2nd Row 1st Column 20 2nd Column 4 3rd Row 1st Column 30 2nd Column 6 4st Row 1st Column 40 2nd Column 5 5st Row 1st Column 50 2nd Column 3 6st Row 1st Column 80 2nd Column 1 EndTable

30

Construct a box plot from the data below. Start 6 By 5 Matrix 1st Row 1st Column 30 2nd Column 35 3rd Column 38 4st Column 39 5st Column 50 2nd Row 1st Column 51 2nd Column 54 3rd Column 54 4st Column 51 5st Column 63 3rd Row 1st Column 65 2nd Column 66 3rd Column 69 4st Column 70 5st Column 73 4st Row 1st Column 77 2nd Column 80 3rd Column 81 4st Column 81 5st Column 83 5st Row 1st Column 85 2nd Column 87 3rd Column 89 4st Column 90 5st Column 93 6st Row 1st Column 93 2nd Column 95 3rd Column 97 4st Column 99 5st Column 107 EndMatrix

30 54 75 89 107

The normal annual precipitation​ (in inches) is given below for 21 different U.S. cities. Find the​ seventy-eighth percentile, Upper P 78. Start 3 By 7 Matrix 1st Row 1st Column 39.1 2nd Column 16.8 3rd Column 25.4 4st Column 18.6 5st Column 27.1 6st Column 27.8 7st Column 30.6 2nd Row 1st Column 15.8 2nd Column 42.6 3rd Column 18.6 4st Column 13.7 5st Column 19.8 6st Column 32.3 7st Column 10.5 3rd Row 1st Column 14.5 2nd Column 33.6 3rd Column 12.4 4st Column 35.0 5st Column 22.3 6st Column 11.8 7st Column 5 1.7 EndMatrix

33.6

The test scores of 15 students are listed below. Find the third​ decile, Upper D 3. Start 3 By 5 Matrix 1st Row 1st Column 42 2nd Column 45 3rd Column 53 4st Column 56 5st Column 61 2nd Row 1st Column 64 2nd Column 66 3rd Column 69 4st Column 75 5st Column 77 3rd Row 1st Column 85 2nd Column 87 3rd Column 90 4st Column 94 5st Column 95 EndMatrix

61

At one high​ school, the mean time for running the​ 100-yard dash is 15.2 seconds with a standard deviation of 0.9 seconds. The times are very closely approximated by a normal curve. Find the percent of times that are between 14.3 and 16.1 seconds. Round your answer to the nearest whole percent.

68%

What was the total increase in sales for the first 6 months from 2009 to​ 2010?

76000

What were the total sales for​ 2010?

764000

Big Bucks Investment Club has a portfolio that includes stocks from 15 corporations listed on the New York Stock Exchange. The closing prices​ (in dollars) of each stock after​ yesterday's trading are listed below. Start 2 By 8 Matrix 1st Row 1st Column 113 and one eighth 2nd Column 45 3rd Column 22 and one half 4st Column 53 and three eighths 5st Column 23 and one fourth 6st Column 11 and five eighths 7st Column 15 8st Column 36 2nd Row 1st Column 52 and seven eighths 2nd Column 77 and three fourths 3rd Column 62 and one eighth 4st Column 80 and three eighths 5st Column 104 and one fourth 6st Column 9 7st Column 93 8st Column EndMatrix Rank the data from lowest to highest and determine the 3rd​ quartile, Q3.

80 3/8

This​ double-bar graph shows the number of male​ (M) and female​ (F) athletes at a university over a​ four-year period. How many students were involved in athletics in​ 1989?

800

Find the percent of the total area under the curve between z=-2.49 and z=1.19. Round your answer to the nearest tenth of a percent. A.​86.8% B.​11.1% C.​87.7% This is the correct answer. D.​11.3%

87.7%

In a certain distribution of​ numbers, the mean is 50 and the standard deviation is 6. What can you say about the percentage of numbers that lie between 26 and​ 74? Use​ Chebyshev's theorem to solve the problem.

93.8 %

Which box has the highest​ median? Four box plots are over a horizontal axis that has 11 equally spaced tick marks. A box plot labeled "A" has a box that extends from the fourth tick mark to the ninth tick mark with a dashed vertical line segment through the box at the seventh tick mark. Two horizontal line segments extend from the left and right sides of the box to between the third and fourth tick marks, and between the ninth and tenth tick marks, respectively. A box plot labeled "B" has a box that extends from between the fourth and fifth tick marks to the eighth tick mark with a dashed vertical line segment through the box at the sixth tick mark. Two horizontal line segments extend from the left and right sides of the box to the right of the third tick mark, and to the left of the ninth tenth tick mark, respectively. A box plot labeled "C" has a box that extends from the second tick mark to the left of the sixth tick mark with a dashed vertical line segment through the box to the left of the fifth tick mark. Two horizontal line segments extend from the left and right sides of the box to the first tick mark and between the sixth and seventh tick marks, respectively. A box plot labeled "D" has a box that extends from the third tick mark to the eighth tick mark with a dashed vertical line segment through the box at the sixth tick mark. Two horizontal line segments extend from the left and right sides of the box to between the second and third tick marks, and between the tenth and eleventh tick marks, respectively.

A

bi-modal 12.2

A histogram with two peaks (modes)

In a certain​ distribution, the mean is 90 with a standard deviation of 3. At least what fraction of the numbers are between the following pair of​ numbers? 81 and 99

At least eight ninths of the numbers in the distribution are between 81 and 99.

Consider the chart to the right. What is the greatest single expense​ category? To the nearest​ degree, what is the central angle of that​ category's sector?

Choose the correct answer below and fill in the answer box to complete your choice. ​(Round to the nearest degree as​ needed.)

The accompanying data are the daily​ round-trip distances to school​ (in miles) for 30 randomly chosen students attending a community college in a certain state. Construct a​ stem-and-leaf display for the given data in the accompanying table. Treat the ones digit as the leaves. For any​ single-digit data, use a stem of 0.

Construct a​ stem-and-leaf display for the given data.

Classify the random variable as either discrete or continuous. The​ voltage-power production of a nuclear power plant

Continuous

Classify the random variable as either discrete or continuous. The number of freshmen in the required​ course, English 101

Discrete

Classify the random variable as either discrete or continuous. The braking time of a car

Discrete

A company has 15 employees with a salary of ​$21 comma 300​, 9 employees with a salary of ​$24 comma 000, 18 employees with a salary of ​$27 comma 000​, 3 employees with a salary of ​$31 comma 000​, 5 employees with a salary of ​$37 comma 700​, and 1 employee with a salary of ​$147 comma 500.

Find the mean salary for the employees. The mean salary for the employees is ​$28,400

Non-Symmetric 12.2

In distributions skewed to the left (a), the data points start low and gradually go up. In distributions skewed to the right (b), data points go up quickly and then gradually go down. In bimodal distribution (c), data points form two peaks.

Is the midquartile necessarily the same as the​ midrange? Answer yes or no and explain your answer. The definitions of midquartile and midrange are given below. Midquartile equals StartFraction Upper Q 1 plus Upper Q 3 Over 2 EndFraction Midrange equals StartFraction minimum item plus maximum item Over 2 EndFraction

No counterexample is 1,10,11,12,13

In a calculus​ class, Jack Hartig scored 6 on a quiz for which the class mean and standard deviation were 4.5 and 1.9, respectively. Norm Alpina scored 5 on another quiz for which the class mean and standard deviation were 3.8 and 1.8​, respectively. Relatively​ speaking, which student did​ better? Make use of​ z-scores.

Relatively​ speaking, Jack scored better on his quiz.

median 12.2

Step 1 Rank the items (that is, arrange them in numerical order from least to greatest). Step 2 If the number of items is odd, the median is the middle item in the list. Step 3 If the number of items is even, the median is the mean of the two middle items.

A teacher gives a test to a large group of students. The results are closely approximated by a normal curve. The mean is 74 with a standard deviation of 5 The teacher wishes to give​ A's to the top 8 ​% of the students and​ F's to the bottom 8 ​%. A grade of B is given to the next 15​%, with​ D's given similarly. All other students get​ C's. Find the bottom cutoff​ (rounded to the nearest whole​ number) for a B.​ (Hint: Use a table of areas under the standard normal curve to find​ z-scores from known​ A-values.)

The bottom cutoff for a B is 78

The accompanying bar graph shows the gross domestic product for a certain country over a​ six-year period. About what was the gross domestic product in Year 4​?

The gross domestic product in Year 4 is about ​$14,700 billion.

The​ stem-and-leaf display represents scores achieved on a​ 100-point biology exam by the 32 members of the class. Identify the​ mean, median and mode for the data represented. A stem hyphen and hyphen leaf plot has the following data, where the stems are listed first and the leaves are listed second: 4, 7; 5, 1 4 8; 6, 2 3 3 4 4 8 8; 7, 0 1 3 3 4 8 8 8 9; 8, 0 1 2 3 4 8 8; 9, 0 1 3 3 8. 4 75 1 4 86 2 3 3 4 4 8 87 0 1 3 3 4 8 8 8 98 0 1 2 3 4 8 89 0 1 3 3 8

The mean for the data is 74.6. ​(Round to the nearest​ tenth.) The median for the data is 76. ​(Type an integer or a​ decimal.) The mode for the data is 78.

While doing an​ experiment, a physics student recorded the following sequence of elapsed times​ (in seconds) in a lab notebook. 2.12, 26.7​, 2.96​,2.05​, 2.77​,2.21​, 2.33 When reviewing the calculations​ later, the student decided that the entry 26.7 should have been recorded as 2.67 and made that change in the listing. Find the mean for the new list.

The mean is approximately 2.44 seconds.

Six people were asked to determine the amount of money they were​ carrying, to the nearest dollar. The results were ​$38​, ​$64​, ​$46, ​ $58​, ​$41 and ​$47 Compute the mean and standard deviation for the sample. Then multiply each amount by 2​,and compute the mean and standard deviation for the new sample.

The mean is ​$49.00 ​(Round to the nearest cent as​ needed.) The standard deviation is ​$10.04​(Round to the nearest cent as​ needed.) The data sample is then multiplied by 2. The mean of the new data sample is ​$98.00. ​(Round to the nearest cent as​ needed.) The standard deviation of the new data sample is ​$20.08

mean (arithmetic mean) 12.2

The mean of a set of numbers is found by adding all the values in the set and dividing by the number of values 1) most common measure of central tendency "x bar" 2) The mean of n data items x1,x2,..., xn, x sub 1 , comma , x sub 2 , comma dot dot dot comma , x sub n , comma is calculated as follows. "x bar"=(∑x)/n 3) average

On the right are the numbers of customers served by a restaurant on 40 consecutive days.​ (The numbers have been ranked lowest to​ highest.) Find the 4 Superscript th decile.

The number of customers representing the 4 Superscript th decile is 63 .

Suppose 120 geology students measure the mass of an ore sample. Due to human error and limitations in the reliability of the​ balance, not all the readings are equal. The results are found to closely approximate a normal​ curve, with mean 82 g and standard deviation 2g. Use the symmetry of the normal curve and the empirical rule as needed to estimate the number of students reporting readings between 78g and 86g.

The number of students reporting readings between 78g and 86g is 114

Find the percent of area under a normal curve between the mean and - 1.08 standard deviations from the mean.​ (Note that positive indicates above the​ mean, while negative indicates below the​ mean.)

The percentage of area under a normal curve between the mean and minus 1.08 standard deviations is 36.0​%.

Find the range and standard deviation of the set of data. 34​, 25​, 29​, 28​, 28​, 31​,28

The range is 9. The standard deviation is 2.828

The table below shows commonly accepted percentages of occurrence for the various letters in English language usage.​ (Code breakers have carefully analyzed these percentages as an aid in deciphering secret​ codes.) For​ example, notice that E is the most commonly occurring​ letter, followed by​ T, A,​ O, N, and so on. The letters Q and Z occur least often. Referring to Figure​ 5, would you say that the relative frequencies of occurrence of the vowels in the figure 5 were typical or​ unusual? Explain your reasoning.

The relative frequencies were typical. deductive reasoning

If your calculator finds both kinds of standard​ deviation, the sample standard deviation and the population standard​ deviation, which of the two will be a larger number for a given set of​ data? (Hint: Recall the difference between how the two standard deviations are​ calculated.) Fill in the blank below.

The sample standard deviation will be a larger number for a given set of data.

Is it possible to compute the actual standard deviation for this​ sample? Class Limits (Frequency f0 ​21-25 5 ​26-30 8 ​31-35 3 ​36-40 21 ​41-45 12 ​46-50 35 ​51-55 38 ​56-60 20

The standard deviation cannot be calculated for the given

Gabriel and Lucia took a road trip across the country. The room​ costs, in​ dollars, for their overnight stays are listed in the accompanying table. Find the standard deviation of the distribution.

The standard deviation of the distribution is ​$55.47 .

Symmetric 12.2

The three figures all show symmetric formations. In uniform distribution (a), the data points have the same vertical value. In binomial distribution (b), data points go up, hit a peak, and then go down. In bi-modal distribution (c), data points form two peaks.

The table on the right shows last initials of basketball players and the number of games played by each. Find the​ z-score for player Upper H​'s games played.

What is player Upper H​'s ​z-score? 0.64

In​ nutrition, the recommended daily allowance​ (RDA) of a vitamin is a number set by the government as a guide to an​ individual's daily vitamin intake.​ Actually, vitamin needs vary drastically from person to​ person, but the needs are very closely approximated by a normal curve. To calculate the​ RDA, the government first finds the average need for vitamins among people in the population and then the standard deviation. The RDA is defined as the mean plus 2.5 times the standard deviation. Find the recommended daily allowance for a vitamin if the mean need and standard deviation are as follows. mean needequals 800 unitsstandard deviationequals 53 units

What is the recommended daily allowance for the​ vitamin? 932.5 units

Use the system shown to the right for assigning grades to students. Is the system more likely fair in a large freshman class in psychology than in a graduate seminar of five​ students?

Yes, because in a large freshman

skewed to the left 12.2

a non-symmetric distribution with a tail extending out to the left shaped like a J

central tendency 12.2

a traditional measurement of mode

Simpson's paradox 12.2

a trend appears in different groups of data but disappears when they are combined

Two samples are given. Find each​ sample's ​a) standard deviation and ​b) coefficient of variation. Then decide ​c) which sample has the higher​ dispersion, and ​d) which sample has the higher relative dispersion.

a) What are the sample standard​ deviations? sSubscript Upper A equals2.68 ​(Do not round until the final answer. Then round to the nearest hundredth as​ needed.) sSubscript Upper B equals3.74 ​(Do not round until the final answer. Then round to the nearest hundredth as​ needed.) ​b) What are the sample coefficients of​ variation? VSubscript Upper A equals55.9 ​(Round the final answer to the nearest tenth as needed. Round all intermediate values to the nearest thousandth as​ needed.) VSubscript Upper B equals62.4 ​(Round the final answer to the nearest tenth as needed. Round all intermediate values to the nearest thousandth as​ needed.) ​c) Which sample has the higher​ dispersion?

In a certain distribution of​ numbers, the mean is 50 and the standard deviation is 6. What can you say about the fraction of numbers that lie between 32 and​ 68? Use​ Chebyshev's theorem to solve the problem.

at least 8/9

Identify the variable quantity as discrete or continuous. the number of heads in 50 tossed coins

discrete

skewed to the right 12.2

non-symmetric distribution with a tail extending to the left

The​ "skewness coefficient" is defined as shown​ below, where x overbar is the​ mean, Upper Q 2 is the second​ quartile, and s is the standard deviation. SK equals StartFraction 3 times left parenthesis x overbar minus Upper Q 2 right parenthesis Over s EndFraction Is this a measure of individual data items or of the overall​ distribution?

overall distribution

The​ mean, as a measure of central​ tendency, is highly sensitive to extreme values. Which measure of dispersion would be more sensitive to extreme​ values?

range is more sensitive to extreme values. The range is defined as difference between the 2 most extreme....

symmetry in data sets 12.2

the most useful way to analyze a data set often depends on the distribution

cumulative frequency 12.2

the sum of the frequencies for that class and all previous classes

mode 12.2

the value that occurs most often

weighted mean 12.2

the weighted mean of a group of (weighted) items is the sum of all products of items times weighting factors, divided by the sum of all weighting factors

Find the​ z-score that best satisfies the condition. 36​% of the total area is to the left of z.

z= -0.36