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statistics
elementary statistics a step by step approach
Elementary Statistics A Step By Step Approach 9th Edition Allan G. Bluman - Solutions
Sometimes a researcher must decide whether a variable is normally distributed. There are several ways to do this. One simple but very subjective method uses special graph paper, which is called normal probability paper. For the distribution of systolic blood pressure readings given in Chapter 3 of
Determine whether each statement is true or false. If the statement is false, explain why.The total area under a normal distribution is infinite.
A study found that 1% of Social Security recipients are too young to vote. If 800 Social Security recipients are randomly selected, find the mean, variance, and standard deviation of the number of recipients who are too young to vote.
The ages of the Vice Presidents of the United States at the time of their death are listed below. Use the data to construct a frequency distribution. Use 6 classes. The data for this exercise will be used for Exercises 8, 10, and 12. 51 68 79 70 71 66 62 63 68 57 57 71 60 85 64 66 77 93 70 90 83 80
A questionnaire on housing arrangements showed this information obtained from 25 respondents. Construct a frequency distribution for the data (H = house, A = apartment, M = mobile home, C = condominium). These data will be used in Exercise 19. нс н MH A C с C с C с M с A А M М A A C
Use the data collected in data project 5 of Chapter 2 regarding delegates. Use the formulas for population mean and standard deviation to compute the parameters for all 50 states. What is the z score associated with California? Delaware? Ohio? Which states are more than 2 standard deviations from
A probability distribution can be written in formula notation such as P(X)= 1/X, where X = 2, 3, 6. The distribution is shown as follows:For Exercises write the distribution for the formula and determine whether it is a probability distribution.P(X) = X/(X + 2) for X = 0, 1, 2 X P(X) 2112 2
A probability distribution can be written in formula notation such as P(X)= 1/X, where X = 2, 3, 6. The distribution is shown as follows:For Exercises write the distribution for the formula and determine whether it is a probability distribution.P(X) = X/7 for X = 1, 2, 4 X P(X) 2112 2
A probability distribution can be written in formula notation such as P(X)= 1/X, where X = 2, 3, 6. The distribution is shown as follows:For Exercises write the distribution for the formula and determine whether it is a probability distribution.P(X) = X + 0.1 for X = 0.1, 0.02, 0.04 X P(X) 2112 2 3
About 35% of Americans abstain from the consumption of alcohol. If Americans are selected at random, find the probability that the 10th person selected will be the first one who doesn’t drink alcohol.
A probability distribution can be written in formula notation such as P(X)= 1/X, where X = 2, 3, 6. The distribution is shown as follows:For Exercises write the distribution for the formula and determine whether it is a probability distribution.P(X) = X/6 for X = 1, 2, 3 X P(X) 2112 2
A probability distribution can be written in formula notation such as P(X)= 1/X, where X = 2, 3, 6. The distribution is shown as follows:For Exercises write the distribution for the formula and determine whether it is a probability distribution.P(X) = X for X = 0.2, 0.3, 0.5 X P(X) 2112 2
Is this a binomial distribution? Explain. X P(X) 0 0.064 1 0.288 2 0.432 3 0.216
A youth group has 8 boys and 6 girls. If a slate of 4 officers is selected, find the probability that exactlya. 3 are girlsb. 2 are girlsc. 4 are boys
A probability distribution can be written in formula notation such as P(X)= 1/X, where X = 2, 3, 6. The distribution is shown as follows:For Exercises write the distribution for the formula and determine whether it is a probability distribution.P(X) = X/6 for X = 3, 4, 7 X P(X) 2112 2
About 4% of the citizens of the United States have type AB blood. If an agency needs type AB blood and donors come in at random, find the probability that the sixth person is the first person with type AB blood.
There are 48 raincoats for sale at a local men’s clothing store. Twelve are black. If 6 raincoats are selected to be marked down, find the probability that exactly 3 will be black.
In a Christmas display, the probability that all lights are the same color is 0.50; that 2 colors are used is 0.40; and that 3 or more colors are used is 0.10. If a sample of 10 displays is selected, find the probability that 5 have only 1 color of light, 3 have 2 colors, and 2 have 3 or more
The probability that a person will make 0, 1, 2, or 3 errors on his or her income tax return is 0.50, 0.30, 0.15, and 0.05, respectively. If 30 claims are selected, find the probability that 15 will contain 0 errors, 8 will contain 1 error, 5 will contain 2 errors, and 2 will contain 3 errors.
If 8% of the population of trees are elm trees, find the probability that in a sample of 100 trees, there are exactly 6 elm trees. Assume the distribution is approximately Poisson.
In a 2011 survey, 58% of American adults said they use the Internet. If 20 American adults are selected at random, find the probability that exactly 12 will say they use the Internet.
Sports Scores Hot Line receives, on the average, 8 calls per hour requesting the latest sports scores. The distribution is Poisson in nature. For any randomly selected hour, find the probability that the company will receivea. At least 8 callsb. 3 or more callsc. At most 7 calls
In 2009 the percentage of the U.S. population who was foreign-born was 12.2. Choose 60 U.S. residents at random. How many would you expect to be American-born? Find the mean, variance, and standard deviation for the number who are foreign-born.
If 40% of all commuters ride to work in carpools, find the probability that if 8 workers are selected, 5 will ride in carpools.
If 80% of the applicants are able to pass a driver’s proficiency road test, find the mean, variance, and standard deviation of the number of people who pass the test in a sample of 300 applicants.
A person works in a large home improvement store and approaches customers to tell them about the store’s carpet sale. He then asks them if they would like to talk to a sales representative. From past experience, the person has found that the probability of getting a “yes” is about 0.32. Find
A history class has 75 members. If there is a 12% absentee rate per class meeting, find the mean, variance, and standard deviation of the number of students who will be absent from each class.
A person selects a card from an ordinary deck of cards. If it is a black card, she wins $2. If it is a red card between or including 3 and 7, she wins $10. If it is a red face card, she wins $25; and if it is a black jack, she wins an extra $100. Find the expectation of the game.
The probabilities of a return on an investment of $5000, $7000, and $9000 are1/2, 3/8, and 1/8, respectively.For Exercises construct a probability distribution for the data and draw a graph for the distribution.
A plate of hors d’oeuvres contains two types of filled puff pastry chicken and shrimp. The entire platter contains 15 pastries— 8 chicken and 7 shrimp. From the outside the pastries appear identical, and they are randomly distributed on the tray. Choose 3 at random; what is the probability that
There are 6 playing cards placed face down in a box. They are the 4 of diamonds, the 5 of hearts, the 2 of clubs, the 10 of spades, the 3 of diamonds, and the 7 of hearts. A person selects a card. Find the expected value of the draw.
A roulette wheel has 38 numbers, 1 through 36, 0, and 00. One-half of the numbers from 1 through 36 are red, and the other half are black; 0 and 00 are green. A ball is rolled, and it falls into one of the 38 slots, giving a number and a color. The payoffs (winnings) for a $1 bet are as follows:If
The number of calls received per day at a crisis hot line is distributed as follows:Find the mean, variance, and standard deviation of the distribution. Number X 30 Probability P(X) 0.05 0.21 33 34 0.38 0.25 0.11 31 32
During a recent CD sale at Matt’s Music Store, the number of CDs customers purchased was distributed as follows:Find the mean, variance, and standard deviation of the distribution. Number X 0 1 2 Probability P(X) 0.10 0.23 0.31 3 4 0.27 0.09
Find the mean, variance, and standard deviation for each of the values of n and p when the conditions for the binomial distributions are met.a. n = 1000, p = 0.1b. n = 500, p = 0.25c. n = 50, p = 2/5d. n = 36, p = 1/6
If 80% of job applicants are able to pass a computer literacy test, find the mean, variance, and standard deviation of the number of people who pass the examination in a sample of 150 applicants.
The number of fire calls the Conestoga Valley Fire Company receives per day is distributed as follows:Construct a graph for the data. Number X 5 6 7 8 9 Probability P(X) 0.28 0.32 0.09 0.21 0.10
For Exercises state whether the variable is discrete or continuous.The number of mathematics majors in your school
For Exercises state whether the variable is discrete or continuous.The weight of an automobile
For exercises determine if the distribution represents a probability distribution. If not, state why. X P(X) 4 1 6 8 3 12 12 호 16 12
For exercises determine if the distribution represents a probability distribution. If not, state why. X P(X) 50 0.5 75 0.2 100 0.3
For Exercises state whether the variable is discrete or continuous.The number of cheeseburgers a fast-food restaurant serves each day
In 2010 almost 15 million U.S. workers belonged to trade unions, constituting 11.9% of the total labor force. Choose 15 U.S. workers at random. What is the probability that exactly one-third of them belong to a trade union? At least one-third? What is the probability that at least 9 did not
For exercises determine if the distribution represents a probability distribution. If not, state why. X P(X) 3 0.3 6 0.5 9 0.1 12 0.08 15 0.02
For exercises determine if the distribution represents a probability distribution. If not, state why. X P(X) 1 2 | 3 ننا 4 ترال
For Exercises determine whether the distribution represents a probability distribution. If it does not, state why. X P(X) 1 0.4 2 0.3 3 0.2 4 1
A craft store has 25 assorted grab bags on sale for $3.00 each. Fifteen of the bags contain $3.00 worth of merchandise, six contain $2.00 worth, two contain $5.00 worth of merchandise, and there are one each containing $10.00 and $20.00 worth of merchandise. Suppose that you purchase one bag; what
The number of trials for a binomial experimenta. Can be infiniteb. Is unchanged c. Is unlimitedd. Must be fixed
How many outcomes are there in a binomial experiment?a. 0b. 1 c. 2d. It varies.
For Exercises determine whether the distribution represents a probability distribution. If it does not, state why. X P(X) -2 0.3 0 0.4 2 0.2 5 0.1
What is the sum of the probabilities of all outcomes in a probability distribution?a. 0b. 1/2c. 1d. It cannot be determined.
Find each probability P(X; λ) using Table C in Appendix A.a. P(10; 7)b. P(9; 8)c. P(3; 4)Data from in Table C Appendix A TABLE C The Poisson
A television commercial claims that 1 out of 5 of “today’s marriages” began as an online relationship. Assuming that this is true, calculate the following for eight randomly selected “today’s marriages.”a. The probability that at least one began onlineb. The probability that two or
One requirement for a probability distribution is that the sum of all the events in the sample space equal________ .
Suppose that we wanted to check the occurrence of leading digits in real-life data such as stock prices, population numbers, death rates, lengths of rivers to see if they occur randomly. Disregarding zero as a leading digit, we might expect the other nine to occur with equal likelihood. Construct
Find each probability P(X; λ), using Table C in Appendix A.a. P(5; 4)b. P(2; 4)c. P(6; 3)Data from in Table C Appendix A TABLE C The Poisson
For Exercises determine whether the distribution represents a probability distribution. If it does not, state why. X P(X) 3 0.3 6 0.5 8 0.7 12 -0.8
Have each student in class toss 4 coins on her or his desk, and note how many heads are showing. Create a frequency table displaying the results. Compare the frequency table to the theoretical probability distribution for the outcome when 4 coins are tossed. Find the mean for the frequency table.
The mean for a binomial variable can be found by using the expression _________ .
According to Mendel’s theory, if tall and colorful plants are crossed with short and colorless plants, the corresponding probabilities are 9/16, 3/16, 3/16, and 1/16 for tall and colorful, tall and colorless, short and colorful, and short and colorless, respectively. If 8 plants are selected,
What is a probability distribution? Give an example.
Find out what percentage of citizens in your state is registered to vote. Assuming that this is a binomial variable, what would be the mean number of registered voters in a random group of citizens with a sample size equal to the number of students in your class? Also determine the standard
What is the expected value of the game of Chuck-a-Luck if a player bets $1.00 on one number?
Random variable values are determined by___________ .
In a magazine survey, 60% of respondents said that they use reusable grocery bags; 32%,plastic; and 8%, paper. In a random sample of 10 grocery shoppers, what is the probability that 6 will use reusable bags and that 2 each will request paper or plastic?
Use Red Cross data to determine the percentage of the population with an Rh factor that is positive (A, B, AB, or O blood types). Use that value for p. How many students in your class have a positive Rh factor? Is this an unusual amount?
In the game Chuck-a-Luck, three dice are rolled. A player bets a certain amount (say $1.00) on a number from 1 to 6. If the number appears on 1 die, the person wins $1.00. If it appears on 2 dice, the person wins $2.00, and if it appears on all 3 dice, the person wins $3.00. What are the chances of
A binomial experiment has a fixed number of trials.
Use your most recent itemized phone bill for the data in this problem. Assume that incoming and outgoing calls are equal in the population (why is this a reasonable assumption?). This means assume p 0.5. For the number of calls you made last month, what would be the mean number of outgoing calls
If you played the same four-digit number every day (or any four-digit number for that matter) in the Big 4, how often (in years) would you win, assuming you have average luck?
For Exercises determine whether the distribution represents a probability distribution. If it does not, state why. X P(X) 8 ko 12 16 금 12 20 금
When the binomial distribution is used, the outcomes must be dependent.
Give three examples of a discrete random variable.
Baseball, hockey, and basketball all use a seven-game series to determine their championship. Find the probability that with two evenly matched teams a champion will be found in 4 games. Repeat for 5, 6, and 7 games. Look at the historical results for the three sports. How do the actual results
Which of the following are binomial experiments or can be reduced to binomial experiments?a. Testing one brand of aspirin by using 10 people to determine whether it is effectiveb. Asking 100 people if they smokec. Checking 1000 applicants to see whether they were admitted to White Oak Colleged.
Use the multinomial formula and find the probabilities for each.a. n = 3, X1 = 1, X2 = 1, X3 = 1, p1 = 0.5, p2 = 0.3, p3 = 0.2b. n = 5, X1 = 1, X2 = 3, X3 = 1, p1 = 0.7, p2 = 0.2, p3 = 0.1c. n = 7, X1 = 2, X2 = 3, X3 = 2, p1 = 0.4, p2 = 0.5, p3 = 0.1
For Exercises determine whether the distribution represents a probability distribution. If it does not, state why. X P(X) 5 0.3 10 0.4 15 0.1
For Exercises determine whether the distribution represents a probability distribution. If it does not, state why. X P(X) 1 12 312
The expected value of a random variable can be thought of as a long-run average.
Use information from the Red Cross to create a pie chart depicting the percentages of Americans with various blood types. Also find information about blood donations and the percentage of each type donated. How do the charts compare? Why is the collection of type O blood so important?
In the Big 4 lottery, for a bet of $100, the payoff is $5000. What is the expected value of winning? Is it worth it?
The number of courses a student is taking this semester is an example of a continuous random variable.True or False
When the mean is computed for individual data, all values in the data set are used.
One-half of all the data values will fall above the mode, and one-half will fall below the mode.
Define quartile.
Shown are the ten U.S. cities (with population over 100,000) with the fewest number of violent crimes reported in 2010. Find the mean, median, mode, and midrange of the data. Temecula, CA Murriefa, CA Surprise, AZ Round Rock, TX Frisco, TX 74 99 106 116 119 Irvine, CA Cary, NC Amherst, NY Simi
The graduation rates of several large state schools are shown below. Identify the five number summary and the interquartile range, and draw a boxplot.59.0 64.0 48.0 40.4 69.0 40.0 70.0 60.077.0
Generally, Greek letters are used to represent _________, and Roman letters are used to represent _________.
The positive square root of the variance is called the _________.
Room and board costs for selected schools are summarized in this distribution. Find the approximate cost of room and board corresponding to each of the following percentiles.a. 30th percentileb. 50th percentilec. 75th percentiled. 90th percentileUsing the same data, find the approximate percentile
The airborne speeds in miles per hour of 21 planes are shown. Find the approximate values that correspond to the given percentiles by constructing a percentile graph.a. 9thb. 20thc. 45thd. 60the. 75thUsing the same data, find the approximate percentile ranks of the following speeds in miles per
The symbol for the population standard deviation is _________.
An extremely high or extremely low data value is called a(n) _________.
How many ways can a person select 3 coins from a box consisting of a penny, a nickel, a dime, a quarter, a half-dollar, and a one-dollar coin?
How many different ways can a researcher select 5 rats from 20 rats and assign each to a different test?
How many ways can a person select 6 candy bars from a list of 10 and 6 salty snacks from a list of 12 to put in a vending machine?
How many ways can a person select 7 television commercials from 11 television commercials?
If a die is rolled 3 times, find the probability of getting at least 1 even number.
A local television station must show commercial X twice, commercial Y twice, and commercial Z three times during a 2-hour show. How many different ways can this be done?
A toy store manager wants to display 7 identical stuffed dogs, 4 identical stuffed cats, and 3 identical stuffed teddy bears on a shelf. How many different arrangements can be made?
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