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elementary statistics
Elementary Statistics Picturing The World 5th Edition Ron Larson, Betsy Farber - Solutions
Conference A math conference has an attendance of 4950 people. Of these, 2110 are college professors and 2575 are female. Of the college professors, 960 are female. (a) Are the events “selecting a female” and “selecting a college professor” mutually exclusive? Explain. (b) The conference
Audit During a 52-week period, a company paid overtime wages for 18 weeks and hired temporary help for 9 weeks. During 5 weeks, the company paid overtime and hired temporary help. (a) Are the events “selecting a week in which overtime wages were paid” and “selecting a week in which temporary
Event A: Randomly select a person between 18 and 24 years old. Event B: Randomly select a person who drives a convertible.
Event A: Randomly select a student with a birthday in April. Event B: Randomly select a student with a birthday in May.
Event A: Randomly select a member of the U.S. Congress. Event B: Randomly select a male U.S. Senator.
Event A: Randomly select a female public school teacher. Event B: Randomly select a public school teacher who is 25 years old.
Recognizing Mutually Exclusive Events In Exercises 9–12, decide if the events are mutually exclusive. Explain your reasoning.
decide if the events shown in the Venn diagram are mutually exclusive. Explain your reasoning.
If events A and B are mutually exclusive, then Graphical Analysis In Exercises 7 and 8,
The probability that event A or event B will occur is
If two events are independent, then they are also mutually exclusive.
If two events are mutually exclusive, they have no outcomes in common.
List examples of (a) two events that are mutually exclusive. (b) two events that are not mutually exclusive. True or False? In Exercises 3–6, determine whether the statement is true or false. If it is false, explain why.
If two events are mutually exclusive, why is
The odds of winning an event A are Show that the probability of event A is given by P1A2 = p p + q
A card is picked at random from a standard deck of 52 playing cards. Find the odds that it is not a spade.
The odds of an event occurring are Find (a) the probability that the event will occur and (b) the probability that the event will not occur.
The probability of winning an instant prize game is The odds of winning a different instant prize game are 1 10. If you want the best chance of winning, which game should you play? Explain your reasoning.
A beverage company puts game pieces under the caps of its drinks and claims that one in six game pieces wins a prize. The official rules of the contest state that the odds of winning a prize are Is the claim “one in six game pieces wins a prize” correct? Why or why not?
Rolling a Pair of Dice You roll a pair of six-sided dice and record the sum. (a) List all of the possible sums and determine the probability of rolling each sum. (b) Use a technology tool to simulate rolling a pair of dice and recording the sum 100 times. Make a tally of the 100 sums and use these
The probability of randomly choosing a smoker whose mother also smoked (Assume that you are choosing from the population of all smokers.) EXTENDING CONCEPTS
The probability of randomly choosing a tea drinker who has a college degree (Assume that you are choosing from the population of all tea drinkers.)
Individual Stock Price An individual stock is selected at random from the portfolio represented by the box-and-whisker plot shown. Find the probability that the stock price is (a) less than $21, (b) between $21 and $50, and (c) $30 or more. Writing In Exercises 73 and 74, write a statement that
College Football A stem-and-leaf plot for the number of touchdowns scored by all NCAA Division I Football Bowl Subdivision teams is shown. If a team is selected at random, find the probability the team scored (a) at least 51 touchdowns, (b) between 20 and 30 touchdowns, inclusive, and (c) more than
Find the probability that a worker chosen at random was not employed in the agriculture, forestry, fishing, and hunting industry.
Find the probability that a worker chosen at random was not employed in the services industry.
Find the probability that a worker chosen at random was employed in the manufacturing industry.
Find the probability that a worker chosen at random was employed in the services industry.
Genetics There are six basic types of coloring in registered collies: sable (SSmm), tricolor (ssmm), trifactored sable (Ssmm), blue merle (ssMm), sable merle (SSMm), and trifactored sable merle (SsMm). The Punnett square at the left shows the possible coloring of the offspring of a trifactored
Genetics A Punnett square is a diagram that shows all possible gene combinations in a cross of parents whose genes are known. When two pink snapdragon flowers (RW) are crossed, there are four equally likely possible outcomes for the genetic makeup of the offspring: red (RR), pink (RW), pink (WR),
Can any of the events in Exercises 59–62 be considered unusual? Explain.
Can any of the events in Exercises 55–58 be considered unusual? Explain.
a high school diploma.
a master’s degree.
an associate’s degree.
a doctorate.
not between 45 and 64 years old Using a Bar Graph to Find Probabilities In Exercises 59–62, use the following bar graph, which shows the highest level of education received by employees of a company. Find the probability that the highest level of education for an employee chosen at random is
not between 21 and 24 years old
between 35 and 44 years old
between 18 and 20 years old
What is the probability that a voter chosen at random did not vote for a Democratic representative in the 2008 election? (Source: Federal Election Commission) Using a Frequency Distribution to Find Probabilities In Exercises 55–58, use the frequency distribution at the left, which shows the
What is the probability that a registered voter in Virginia voted in the 2009 gubernatorial election?
Machine Part Suppliers Your company buys machine parts from three different suppliers. Make a tree diagram that shows the three suppliers and whether the parts they supply are defective. Graphical Analysis In Exercises 53 and 54, use the diagram to answer the question.
List the outcome(s) of the event “It rains on at least one day.”
List the outcome(s) of the event “It rains on exactly one day.”
List the outcome(s) of the event “It rains all three days.”
List the sample space.
Security System An access code consists of a letter followed by four digits. Any letter can be used, the first digit cannot be 0, and the last digit must be even. (a) Find the number of possible access codes. (b) What is the probability of randomly selecting the correct access code on the first
Security System The access code for a garage door consists of three digits. Each digit can be any number from 0 through 9, and each digit can be repeated. (a) Find the number of possible access codes. (b) What is the probability of randomly selecting the correct access code on the first try? (c)
Event D: not rolling a number less than 6 and the spinner landing on yellow
Event C: rolling a number less than 6 and the spinner landing on yellow
Event B: rolling an odd number and the spinner landing on green
Event A: rolling a 5 and the spinner landing on blue
Find the probability of selecting a number that is not divisible by 1000.
Find the probability of selecting a number divisible by 1000.
Find the probability of selecting a number greater than 1000.
Find the probability of selecting a number less than 1000.
The probability of choosing 6 numbers from 1 to 40 that match the 6 numbers drawn by a state lottery is 1>3,838,380 L 0.00000026. Finding Probabilities In Exercises 37–40, consider a company that selects employees for random drug tests. The company uses a computer to randomly select employee
According to company records, the probability that a washing machine will need repairs during a six-year period is 0.10.
Event F: rolling a number divisible by 5 Classifying Types of Probability In Exercises 35 and 36, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.
Event E: rolling a prime number
Event D: rolling an even number
Event C: rolling a number greater than 4
Event B: rolling a 10
Event A: rolling a 2
True or False Quiz Assuming that no questions are left unanswered, in how many ways can a six-question true-false quiz be answered? Classical Probabilities In Exercises 29–34, a probability experiment consists of rolling a 12-sided die. Find the probability of each event.
Realty A realtor uses a lock box to store the keys for a house that is for sale. The access code for the lock box consists of four digits.The first digit cannot be zero and the last digit must be even. How many different codes are available?
Menu A restaurant offers a $12 dinner special that has 5 choices for an appetizer, 10 choices for entrées, and 4 choices for dessert. How many different meals are available if you select an appetizer, an entrée, and a dessert?
Job Openings A software company is hiring for two positions: a software development engineer and a sales operations manager. How many ways can these positions be filled if there are 12 people applying for the engineering position and 17 people applying for the managerial position?
You randomly select one card from a standard deck. Event B is selecting a ten of diamonds.
You randomly select one card from a standard deck. Event A is selecting an ace.
A computer is used to randomly select a number between 1 and 4000. Event B is selecting a number less than 500.
A computer is used to randomly select a number between 1 and 4000. Event A is selecting 253.
Rolling a pair of six-sided dice
Determining a person’s blood type (A, B, AB, O) and Rh-factor (positive, negative)
Tossing three coins
Drawing one card from a standard deck of cards
Guessing a student’s letter grade (A, B, C, D, F) in a class
Guessing the initial of a student’s middle name
Five of the 100 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly select an item that is not defective?
A game show contestant must randomly select a door. One door doubles her money while the other three doors leave her with no winnings. What is the probability she selects the door that doubles her money?
A random number generator is used to select a number from 1 to 100. What is the probability of selecting the number 153?
You toss a coin and randomly select a number from 0 to 9. What is the probability of getting tails and selecting a 3?
If an event is almost certain to happen, its complement will be an unusual event.
A probability of indicates an unusual event.
You toss a fair coin nine times and it lands tails up each time. The probability it will land heads up on the tenth flip is greater than 0.5.
If you roll a six-sided die six times, you will roll an even number at least once.
Use your own words to describe the law of large numbers. Give an example.
Explain why the following statement is incorrect: The probability of rain tomorrow is 150%.
Determine whi1. ch of the following numbers could not represent the probability of an event. Explain your reasoning. (a) 33.3% (b) (c) 0.0002 (d) 0 (e) (f)
Describe the shape of the distribution in the histogram you made in Exercise 4.Is the distribution symmetric, uniform, or skewed?
Describe the shape of the distribution in the histogram you made in Exercise 3.Is the distribution symmetric, uniform, or skewed?
Four test scores are given. The first 3 test scores are 20% of the final grade, and the last test score is 40% of the final grade. Find the weighted mean of the test scores. 96 85 91 86
Six test scores are given.The first 5 test scores are 15% of the final grade, and the last test score is 25% of the final grade. Find the weighted mean of the test scores. 78 72 86 91 87 80
16. The following frequency distribution shows the number of magazine subscriptions per household for a sample of 60 households. Find the mean number of subscriptions per household. Number of magazines 01 23456 Frequency 13 9 19 8 5 2 4
Estimate the mean of the frequency distribution you made in Exercise 1
Airport Scanners The responses of 542 adults who were asked whether they approved the use of full-body scanners at airport security checkpoints (Adapted from USA Today/Gallup Poll) Approved: 423 Did not approve: 108 No opinion: 11
Vertical Jumps The vertical jumps (in inches) of a sample of 10 college basketball players at the 2009 NBA Draft Combine (Source: SportsPhenoms,Inc.) 26.0 29.5 27.0 30.5 29.5 25.0 31.5 33.0 32.0 27.5
Make a pie chart of the data set.
Make a Pareto chart of the data set.
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