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elementary statistics

Elementary Statistics Picturing The World 5th Edition Ron Larson, Betsy Farber - Solutions

Describe the weights of the top 10% of the babies born within each gestation period. Explain your reasoning. (a) Under 28 weeks (b) 34 to 36 weeks (c) 41 weeks (d) 42 weeks and over
What percent of the babies born within each gestation period have a low birth weight (under 5.5 pounds)? Explain your reasoning. (a) Under 28 weeks (b) 32 to 33 weeks (c) 40 weeks (d) 42 weeks and over
The distributions of birth weights for three gestation periods are shown. Match the curves with the gestation periods. Explain your reasoning. (a) (b) 5 6 7 8 10 11 Pounds (c) Pounds 5 6 10 11 Pounds 10
Getting at the Concept Why is it correct to say “a” normal distribution and “the” standard normal distribution?
Describe how you can transform a nonstandard normal distribution to a standard normal distribution.
Suppose that the mean number of arrivals per minute is4.(a) What is the probability that three, four, or five customers will arrive during the third minute? (b) What is the probability that more than four customers will arrive during the first minute? (c) What is the probability that more than four
Suppose that the mean number of arrivals per minute is5.What is the probability that 10 customers will arrive during the first minute?
Simulate the setting in Exercise4.Do this by generating a list of 20 random numbers with a Poisson distribution for =5.Then create a table that shows the number of customers waiting at the end of 20 minutes.
Suppose that the mean increases to 5 arrivals per minute. You can still process only four per minute. How many would you expect to be waiting in line after 20 minutes?
Generate a list of 20 random numbers with a Poisson distribution for =4.Create a table that shows the number of customers waiting at the end of 1 through 20 minutes.
MINITAB was used to generate 20 random numbers with a Poisson distribution for =4.Let the random number represent the number of arrivals at the checkout counter each minute for 20 minutes. 3 3 3 3 5 5 67 36 3 5 6 3 4 6 2 2 4 1 During each of the first four minutes, only three customers arrived.
Suppose that the mean number of customers who arrive at the checkout counters each minute i4.Create a Poisson distribution with =4 for x = 0 to20.Compare your results with the histogram shown at the upper right.
A corporation has six male senior executives and four female senior executives. Four senior executives are chosen at random to attend a technology seminar. What is the probability of choosing (a) four men? (b) four women? (c) two men and two women? (d) one man and three women?
In Exercise 4, find the probability of the vending company receiving (a) no defective units. (b) all defective units. (c) at least one good unit.
Decide if the events are mutually exclusive. Then decide if the events are independent or dependent. Explain your reasoning. Event A: A golfer scoring the best round in a four-round tournament Event B: Losing the golf tournament
Which event(s) in Exercise 1 can be considered unusual? Explain your reasoning.
What is the probability that neither the first- nor the second-worst team will get the first pick?Take this quiz as you would take a quiz in class. After you are done, check your work against the answers given in the back of the book.
What is the probability that the team with the worst record will win the third pick, given that the team with the best record, ranked 14th, wins the first pick and the team ranked 2nd wins the second pick?
What is the probability that the team with the worst record will win the second pick, given that the team with the best record, ranked 14th, wins the first pick?
For each team, find the probability that the team will win the first pick.Which of these events would be considered unusual? Explain.
In how many ways can four of the numbers be selected if order is important?
In how many ways can 4 of the numbers 1 to 14 be selected if order is not important? How many sets of 4 numbers are assigned to the 14 teams?
Warehouse A warehouse employs 24 workers on first shift and 17 workers on second shift. Eight workers are chosen at random to be interviewed about the work environment. Find the probability of choosing (a) all first-shift workers. (b) all second-shift workers. (c) six first-shift workers. (d) four
Cards You are dealt a hand of five cards from a standard deck of playing cards. Find the probability of being dealt a hand consisting of (a) four-of-a-kind. (b) a full house, which consists of three of one kind and two of another kind. (c) three-of-a-kind. (The other two cards are different from
(b) Use a technology tool to find the number of ways 15 employees can be chosen from 144 nonminorities. (c) If the committee is chosen randomly (without bias), what is the probability that it contains no minorities? (d) Does your answer to part (c) indicate that the committee selection is biased?
Probability A company that has 200 employees chooses a committee of 15 to represent employee retirement issues. When the committee is formed, none of the 56 minority employees are selected. (a) Use a technology tool to find the number of ways 15 employees can be chosen from
Probability In a state lottery, you must correctly select 5 numbers (in any order) out of 40 to win the top prize. (a) How many ways can 5 numbers be chosen from 40 numbers? (b) You purchase one lottery ticket.What is the probability that you will win the top prize?
What is the probability that none of the 55 people would rate their financial shape as good? (Make the assumption that the 500 people are represented by the pie chart.)
Suppose 55 people are chosen at random from a group of
What is the probability that none of the 80 people would rate their financial shape as fair? (Make the assumption that the 500 people are represented by the pie chart.)
Suppose 80 people are chosen at random from a group of
Suppose 10 people are chosen at random from a group of 1200. What is the probability that all 10 would rate their financial shape as poor? (Make the assumption that the 1200 people are represented by the pie chart.)
Suppose 4 people are chosen at random from a group of 1200. What is the probability that all four would rate their financial shape as excellent? (Make the assumption that the 1200 people are represented by the pie chart.)
Defective Units A shipment of 10 microwave ovens contains two defective units. In how many ways can a restaurant buy three of these units and receive (a) no defective units, (b) one defective unit, and (c) at least two nondefective units? (d) What is the probability of the restaurant buying at
Repairs In how many orders can three broken computers and two broken printers be repaired if (a) there are no restrictions, (b) the printers must be repaired first, and (c) the computers must be repaired first? (d) If the order of repairs has no restrictions and the order of repairs is done at
Area Code An area code consists of three digits. How many area codes are possible if (a) there are no restrictions and (b) the first digit cannot be a 1 or a 0? (c) What is the probability of selecting an area code at random that ends in an odd number if the first digit cannot be a 1 or a 0?
Password A password consists of two letters followed by a five-digit number. How many passwords are possible if (a) there are no restrictions and (b) none of the letters or digits can be repeated? (c) What is the probability of guessing the password in one trial if there are no restrictions?
License Plates In a certain state, each automobile license plate number consists of two letters followed by a four-digit number. How many distinct license plate numbers can be formed if (a) there are no restrictions and (b) the letters O and I are not used? (c) What is the probability of selecting
Employee Selection Four sales representatives for a company are to be chosen to participate in a training program. The company has eight sales representatives, two in each of four regions. In how many ways can the four sales representatives be chosen if (a) there are no restrictions and (b) the
Officers The offices of president, vice president, secretary, and treasurer for an environmental club will be filled from a pool of 14 candidates. Six of the candidates are members of the debate team. (a) What is the probability that all of the offices are filled by members of the debate team? (b)
Jukebox You look over the songs on a jukebox and determine that you like 15 of the 56 songs. (a) What is the probability that you like the next three songs that are played? (Assume a song cannot be repeated.) (b) What is the probability that you do not like the next three songs that are played?
Pizza Toppings A pizza shop offers nine toppings. No topping is used more than once. What is the probability that the toppings on a three-topping pizza are pepperoni, onions, and mushrooms?
Horse Race A horse race has 12 entries. Assuming that there are no ties, what is the probability that the three horses owned by one person finish first, second, and third?
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Soil Samples An environmental agency is analyzing soil samples from 50 farms for lead contamination. Eight of the farms have dangerously high levels of lead. If 10 farms are randomly selected from the sample, how many ways could 2 contaminated farms and 8 noncontaminated farms be chosen? Use a
Water Samples An environmental agency is analyzing water samples from 80 lakes for pollution. Five of the lakes have dangerously high levels of dioxin. If six lakes are randomly selected from the sample, how many ways could one polluted lake and five non-polluted lakes be chosen? Use a technology
Menu A restaurant offers a dinner special that has 12 choices for entrées, 10 choices for side dishes, and 6 choices for dessert. For the special, you can choose one entrée, two side dishes, and one dessert. How many different meals are possible?
Space Shuttle Menu Space shuttle astronauts each consume an average of 3000 calories per day. One meal normally consists of a main dish, a vegetable dish, and two different desserts. The astronauts can choose from 10 main dishes, 8 vegetable dishes, and 13 desserts. How many different meals are
Jury Selection From a group of 40 people, a jury of 12 people is selected. In how many different ways can a jury of 12 people be selected?
Letters In how many distinguishable ways can the letters in the word statistics be written?
Experimental Group In order to conduct an experiment, 4 subjects are randomly selected from a group of 20 subjects. How many different groups of four subjects are possible?
Bracelets You are putting 4 spacers, 10 gold charms, and 8 silver charms on a bracelet. In how many distinguishable ways can the spacers and charms be put on the bracelet?
Assembly Process There are four processes involved in assembling a certain product. These processes can be performed in any order. Management wants to find which order is the least time-consuming. How many different orders will have to be tested?
Lottery Number Selection A lottery has 52 numbers. In how many different ways can 6 of the numbers be selected? (Assume that order of selection is not important.)
Starting Lineup The starting lineup for a softball team consists of 10 players. How many different batting orders are possible using the starting lineup?
Security Code In how many ways can the letters A, B, C, D, E, and F be arranged for a six-letter security code?
Skiing Eight people compete in a downhill ski race. Assuming that there are no ties, in how many different orders can the skiers finish?
Video Games You have seven different video games. How many different ways can you arrange the games side by side on a shelf?
The number of four-letter passwords that can be created when no letter can be repeated USING AND INTERPRETING CONCEPTS
The number of ways 2 captains can be chosen from 28 players on a lacrosse team
The number of ways a four-member committee can be chosen from 10 people
The number of ways eight cars can line up in a row for a car wash
14C7 11P3 In Exercises 15-18, decide if the situation involves permutations, combinations, or neither. Explain your reasoning.
12C6 10C7
7P4 SC4
8. 16 P2
21C8 6P2
8C3
9Ps
7C5=7C2 In Exercises 7-14, perform the indicated calculation.
If you divide the number of permutations of 11 objects taken 3 at a time by 3!, you will get the number of combinations of 11 objects taken 3 at a time.
The number of different ordered arrangements of n distinct objects is n!.
A combination is an ordered arrangement of objects.
When you calculate the number of combinations of r objects taken from a group of n objects, what are you counting? Give an example. True or False? In Exercises 3–6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.
A member of Congress is selected at random. Use the table from Exercise 5 to find the probability of each event. (a) The member is Independent. (b) The member is female and a Republican. (c) The member is male or a Democrat.
Using the same row and column headings as the tables above, create a combined table for Congress.
A senator is selected at random. Find the probability of each event. (a) The senator is male. (b) The senator is not a Democrat. (c) The senator is female or a Republican. (d) The senator is male or a Democrat. (e) Are the events “being female” and “being an Independent” mutually exclusive?
A representative is selected at random. Find the probability of each event. (a) The representative is male. (b) The representative is a Republican. (c) The representative is male given that the representative is a Republican. (d) The representative is female and a Democrat. (e) Are the events
Compare the probabilities from Exercise 1.
Find the probability that a randomly selected representative is female. Find the probability that a randomly selected senator is female.
P(A) 0.38, P(B) = 0.26, P(C) = 0.14, P(A and B) = 0.12, P(A and C) = 0.03, P(B and C) = 0.09, P(A and B and C) = 0.01
P(A) = 0.40, P(B) = 0.10, P(C) = 0.50, P(A and B) = 0.05, P(A and C) = 0.25, P(B and C) = 0.10, P(A and B and C) = 0.03 =
Writing Is there a relationship between independence and mutual exclusivity? To decide, find examples of the following, if possible. (a) Describe two events that are dependent and mutually exclusive. (b) Describe two events that are independent and mutually exclusive. (c) Describe two events that
Eye Survey The table shows the results of a survey that asked 3203 people whether they wore contacts or glasses. A person is selected at random from the sample. Find the probability of each event. (a) The person wears only contacts or only glasses. (b) The person is male or wears both contacts and
Charity The table shows the results of a survey that asked 2850 people whether they were involved in any type of charity work. A person is selected at random from the sample. Find the probability of each event. (a) The person is frequently or occasionally involved in charity work. (b) The person is
Left-Handed People In a sample of 1000 people (525 men and 475 women), 113 are left-handed (63 men and 50 women). The results of the sample are shown in the table. A person is selected at random from the sample. Find the probability of each event. (a) The person is left-handed or female. (b) The
Nursing Majors The table shows the number of male and female students enrolled in nursing at the University of Oklahoma Health Sciences Center for a recent semester. A student is selected at random. Find the probability of each event. (Adapted from University of Oklahoma Health Sciences Center
Olympics The number of responses to a survey are shown in the Pareto chart. The survey asked 1000 U.S. adults if they would watch a large portion of the 2010 Winter Olympics. Each person gave one response. Find each probability. (Adapted from Rasmussen Reports) (a) Randomly selecting a person from
Education The number of responses to a survey are shown in the Pareto chart. The survey asked 1026 U.S. adults how they would grade the quality of public schools in the United States. Each person gave one response. Find each probability. (Adapted from CBS News Poll) (a) Randomly selecting a person
Tacoma Narrows Bridge The percent distribution of the number of occupants in vehicles crossing the Tacoma Narrows Bridge in Washington is shown in the pie chart. Find each probability. (Source: Washington State Department of Transportation) (a) Randomly selecting a car with two occupants (b)
U.S. Age Distribution The estimated percent distribution of the U.S. population for 2020 is shown in the pie chart. Find each probability. (Source: U.S. Census Bureau) (a) Randomly selecting someone who is under 5 years old (b) Randomly selecting someone who is not 65 years or over (c) Randomly
Rolling a Die You roll a die. Find each probability. (a) Rolling a 5 or a number greater than 3 (b) Rolling a number less than 4 or an even number (c) Rolling a 2 or an odd number
Selecting a Card A card is selected at random from a standard deck. Find each probability. (a) Randomly selecting a club or a 3 (b) Randomly selecting a red suit or a king (c) Randomly selecting a 9 or a face card
Can Defects A company that makes soda pop cans finds that the probability of producing a can without a puncture is 0.96, the probability that a can does not have a smashed edge is 0.93, and the probability that a can does not have a puncture and does not have a smashed edge is 0.893. (a) Are the
Carton Defects A company that makes cartons finds that the probability of producing a carton with a puncture is 0.05, the probability that a carton has a smashed corner is 0.08, and the probability that a carton has a puncture and has a smashed corner is 0.004. (a) Are the events “selecting a

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