chapter06 Discrete Probability Distributions.doc

Chapter 6 Discrete Probability Distributions True/False

1. The Poisson probability probability distribution is always always negatively skewed. Answer: False Difficulty: Difficulty: Easy oal: !

". A rando# variable is assigned nu#erical values values based on the outco#es of an e$peri#ent. Answer: True Difficulty: Easy oal: 1

%. A rando# variable represents the outco#es outco#es of an e$peri#ent. Answer: True Difficulty: Easy oal: 1

&. The probability of a particular particular outco#e' designated (' #ust always be between ) and 1)) inclusive. Answer: False Difficulty: Difficulty: Easy oal: 1

*. +f we toss two coins and and count the nu#ber of heads' heads' there could be )' 1 or " heads. ,ince the e$act nu#ber of heads resulting fro# this e$peri#ent is due to chance' the nu#ber of heads appearing is a rando# variable. Answer: True Difficulty: Easy oal: "

!. +f -niue /uying ,ervices has 1)) e#ployees' e#ployees' there #ight be )' 1' "' % up to 1)) e#ployees absent on 0onday. 0onday. +n this case' the day of the week is is the rando# variable. Answer: False Difficulty: Difficulty: Easy oal: " AA,/: AS

2. A discrete rando# variable can have only certain clearly separated separated values. Answer: True Difficulty: Easy oal: "

3. A discrete variable #ay assu#e fractional or deci#al values' values' but they #ust have distance between the#. Answer: True Difficulty: Easy oal: "

4. For a bino#ial distribution' each trial has a known nu#ber nu#ber of successes. For e$a#ple' a four four uestion #ultiple5choice test can only have 6ero' one' two' three and four successes 7nu#ber correct8. Answer: True Difficulty: Easy oal: &

1). The rando# variable for a Poisson probability distribution distribution can assu#e an infinite infinite nu#ber of values.

Statistical Techniques in Business & Economics, Lind/Marchal/Wathen, Lind/Marchal/Wathen, 13/e

32

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Answer: True

Difficulty: Easy

oal: !









11. A probability distribution distribution is a #utually e$clusive listing of e$peri#ental outco#es that can occur by chance and their corresponding probabilities. Answer: True Difficulty: Easy oal: 1

1". To construct construct a bino#ial probability distribution' distribution' the nu#ber of trials and the probability of success #ust be known. Answer: True Difficulty: Easy oal: &

1%. The Poisson probability probability distribution is a continuous continuous probability distribution. distribution. Answer: False Difficulty: Difficulty: Easy oal: !

1&. +f we #easure the weight of of a car' the variable is is a discrete rando# variable. variable. Answer: False Difficulty: Difficulty: Easy oal: "

1*. A bino#ial distribution distribution has a characteristic that the trials are independent' independent' which #eans that the outco#e of one trial does not affect the outco#e of any other trial. Answer: True Difficulty: Easy oal: &

1!. For a bino#ial distribution' distribution' outco#es of an e$peri#ent are classified into one of two #utually e$clusive categories 7a success or a failure8. Answer: True Difficulty: Easy oal: &

12. For a bino#ial distribution' distribution' the probability of a success stays the sa#e for each trial' but the probability of a failure failure varies fro# trial to trial. trial. Answer: False Difficulty: Difficulty: Easy oal: &

13. For a bino#ial distribution' distribution' the data collected collected are the result of counts. counts. Answer: True Difficulty: Easy oal: &

14. 9hen sa#pling is done without without replace#ent and the outco#es are #easured as either a success or failure' the hypergeo#etric distribution should be applied. Answer: True Difficulty: Easy oal: *

"). A Poisson distribution distribution is a discrete probability probability distribution. distribution. +t has the sa#e four characteristics characteristics as the bino#ial' but in addition' addition' the probability probability of a success is s#all s#all and the nu#ber of trials is relatively relatively large. Answer: True Difficulty: Easy oal: !









"". The #ean of a bino#ial probability distribution distribution can be deter#ined by #ultiplying #ultiplying the probability of a failure by the nu#ber of trials. Answer: False Difficulty: Difficulty: 0ediu# oal: &

"%. A bino#ial distribution is a continuous probability probabilit y distribution. Answer: False Difficulty: Difficulty: Easy oal: &

"&. The bino#ial and Poisson distributions distributions are discrete probability probability distributions. distributions. Answer: True Difficulty: Easy oal: &' !

"*. To construct a bino#ial distribution' distribution' it is necessary to know the total nu#ber of trials and the probability of success success on each trial. Answer: True Difficulty: Easy oal: &

"!. +f the probability probability of of success 7 π 8 re#ains the sa#e' but n increases' the shape of the bino#ial distribution beco#es #ore sy##etrical. Answer: True Difficulty: 0ediu# oal: &

"2. The #ean of a probability probability distribution distribution is called its e$pected value. value. Answer: True Difficulty: Easy oal: 1

"3. The #ean of a bino#ial bino#ial distribution is the the product of n and π . Answer: True Difficulty: Easy oal: &

"4. The variance of a bino#ial bino#ial distribution is found by η π 71 5 π 8. Answer: True Difficulty: 0ediu# oal: &

%). As a general rule of thu#b' if the ite#s selected for a sa#ple are not replaced and the sa#ple si6e is less than * percent of the population' the bino#ial distribution distribution can be used to appro$i#ate the hypergeo#etric hypergeo#etric distribution. distribution. Answer: True Difficulty: 0ediu# oal: * AA,/: REF

%1. +n a Poisson distribution' distribution' the probability probability of success #ay vary fro# trial trial to trial. Answer: False Difficulty: Difficulty: Easy oal: !









%". A #ail5order house' advertising advertising sa#e day service' received a large large nu#ber of co#plaints. co#plaints. A change in the handling of orders was #ade with less than * unfilled orders on hand 7per picker8 at the end of 4* out of every 1)) working days. Freuent checks of unfilled orders at the end of the day revealed that the distribution of unfilled orders appro$i#ated appro$i#ated a Poisson distribution; that is' #ost of the days there were no unfilled orders; so#e of the days there was one order' and so on. ,ince the average nu#ber of unfilled orders per picker was ".)' the #ail5order house lived up to its goal. Answer: True Difficulty:
%%. The bino#ial probability probability distribution is always always negatively skewed. Answer: False Difficulty: Difficulty: Easy oal: &

%&. The e$pected value of su##ing two rando# variables variables is the su# of their e$pected values. Answer: True Difficulty: Difficulty: Easy oal: ovariance

%*. +f the covariance between two two rando# variables is 6ero' 6ero' the two variables are related. related. Answer: False Difficulty: Difficulty: Easy oal: ovariance

%!. The variance of the su# of two rando# variables is the su# of their variances plus two ti#es the covariance. Answer: True Difficulty: Difficulty: Easy oal: ovariance

%2. +f the covariance between two two rando# variables is 6ero' 6ero' the two variables are not not related. Answer: True Difficulty: Difficulty: Easy oal: ovariance

Multiple Choice

%3. +f the variance of a probability was co#puted to be %.! gra#s' what is the standard deviation= deviation= A8 ).! /8 1.4 8 !.) D8 1".4! Answer: / Difficulty: Difficulty: Easy oal: %

%4. ,i$ty percent of the custo#ers custo#ers of a fast food chain order the the 9hopper' 9hopper' french fries and a drink. +f a rando# sa#ple of 1* cash register receipts is selected' what is the probability that 1) or #ore will show that the above three food ite#s were ordered= A8 1'))) /8 ).13!









&). >udging fro# recent e$perience' * percent of the co#puter keyboards keyboards produced by an auto#atic' high5speed #achine are defective. 9hat is the probability that out of si$ keyboards keyboards selected at rando#' e$actly 6ero keyboards will be defective= A8 ).))1 /8 ).1!2 8 ).2%* D8 ).*)) Answer:  Difficulty: Difficulty:
&1. The probabilities and the nu#ber nu#ber of auto#obiles lined up at a ?akeside @lds at opening ti#e 72:%) a.#.8 for service are:

A u # b e r 1 " % &

P ro b a b ility ) .) * ) .% ) ) .& ) ) ." *

@n a typical day' how #any auto#obiles should ?akeside @lds e$pect to be lined up at opening= A8 1).)) /8 1.)) 8 ".3* D8 1.4! Answer:  Difficulty: Difficulty: 0ediu# oal: %

&". @n a very hot su##er day' * percent of the production production e#ployees at 0idland ,tates ,teel are absent fro# work. The production e#ployees e#ployees are rando#ly selected for a special in5depth study on absenteeis#. absenteeis#. 9hat is the probability of rando#ly selecting 1) production e#ployees on a hot su##er day and finding that none of the# are absent= A8 ).))" /8 ).%&& 8 ).*44 D8 ).1)) Answer:  Difficulty: Difficulty:
&%. The #arketing depart#ent of a nationally known known cereal #aker plans to conduct a national survey to find out whether or not consu#ers of flake cereals can distinguish one of their favorite flake cereals. To test the uestionnaire and procedure to be used' eight persons were asked to cooperate in an e$peri#ent. Five very s#all bowls of flake cereals were placed in front of a person. The bowls were labeled A' A' /' ' D and E. The person was infor#ed infor#ed that only one bowl bowl contained his or her favorite favorite flake cereal. ,uppose that the eight persons in the e$peri#ent were unable to identify their favorite cereal and Bust guessed which bowl it was in. 9hat is the probability that none of the eight guessed guessed correctly= A8 ).1!3











&&. An insurance insurance agent has appoint#ents appoint#ents with four prospective prospective clients to#orrow. to#orrow. Fro# past e$perience the agent knows that the probability probability of #aking a sale on any appoint#ent is 1 out of *. -sing the rules of probability' probability' what is the likelihood likelihood that the agent will will sell a policy to % of of the & prospective clients= clients= A8 )."*) /8 ).*)) 8 ).&1) D8 ).)"! Answer: D Difficulty: Difficulty: 0ediu# oal: *

&*. ,weetwater C Associates Associates write weekend weekend trip insurance at a very very no#inal charge. ecords show that the probability that a #otorist will have an accident during the weekend and f ile a clai# is ).)))*. ,uppose they wrote &)) policies for the co#ing weekend' what is the probability that e$actly two clai#s will be filed= A8 ).3132 /8 )."*)) 8 ).)1!& D8 ).)))1 Answer:  Difficulty: Difficulty: 0ediu# oal: !

&!. +n which of the following discrete distribution distribution does the probability of of a success vary fro# one trial to the ne$t= A8 /ino#ial /8 Poisson 8
&2. 9hich of the following is a reuire#ent for use of the hypergeo#etric hypergeo#etric distribution= distribution= A8 @nly " possible outco#es /8 Trials Trials are independent 8 Probability of a success is greater greater than 1.) D8 All of of the above above Answer: A Difficulty: 0ediu# oal: *









&4. 9hich one of the following is @T a condition condition of the bino#ial distribution= distribution= A8 +ndependent trials /8 @nly two outco#es 8 Probability of success re#ains re#ains constant fro# trial trial to trial D8 At least least 1) observations observations Answer: D Difficulty: Difficulty: 0ediu# oal: &

*). 9hich is true for a bino#ial bino#ial distribution= distribution= A8 There are three or #ore possible possible outco#es /8 Probability of success re#ains re#ains the sa#e fro# trial to trial trial 8 alue alue of p is eual to 1.*) D8 All of the the above are correct correct Answer: / Difficulty: Difficulty: 0ediu# oal: &

*1. 9hich shape describes describes a Poisson distribution= distribution= A8 Positively skewed /8 egatively skewed 8 ,y##etrical D8 All of of the above above Answer: A Difficulty: Easy oal: !

*". ,ponsors of a local charity decided to attract wealthy patrons patrons to its *))5a5plate dinner by allowing allowing each patron to buy a set of ") tickets for the ga#ing tables. The chance of winning a pri6e for each of the ") plays is *)5*). +f you bought ") tickets' what is the chance of winning 1* or #ore pri6es= A8 )."*) /8 ).)"1 8 ).))! D8 ).2*) Answer: / Difficulty: Difficulty:
*%. 9hat kind of distribution distribution are the bino#ial and Poisson distributions= distributions= A8 Discrete









**. The weight of an offensive lines#an lines#an #ay be ")*.1* pounds' "1)."% pounds' ""*.)* pounds pounds or "14.1& pounds. 9hat 9hat is this an illustration illustration of= A8 ontinuous rando# variable variable /8 Discrete rando# variable variable 8 o#ple#ent rule D8 All of of the above above Answer: A Difficulty: Easy oal: "

*!. arlson >ewelers per#its the return of their dia#ond dia#ond wedding rings' provided the return occurs within two weeks of the purchase date. Their records reveal that 1) percent of the dia#ond wedding rings are returned. Five different custo#ers custo#ers buy five rings. 9hat is the probability probability that none will will be returned= A8 )."*) /8 ).)2% 8 ).*4) D8 ).*)) E8 ).%2" Answer:  Difficulty: Difficulty:
*2. +n a large #etropolitan area' past records revealed that %) percent of all the high school school graduates go to college. Fro# ") graduates selected at rando#' what is the probability that that e$actly 3 will go to college= A8 ).11& /8 ).332 8 ).&)) D8 )."%1 Answer: A Difficulty:
*3. hances are *)5*) that a newborn newborn baby will be a girl. girl. For fa#ilies with five five children' what is the probability that all the children are girls= girls= A8 ).4)) /8 ).)%1 8 ).))1 D8 )."*)









!). The production depart#ent has installed installed a new spray #achine to paint paint auto#obile doors. doors. As is co##on with #ost spray guns' unsightly ble#ishes often appear because of i#proper #i$ture or other proble#s. A worker counted the nu#ber nu#ber of ble#ishes on each door. door. 0ost doors had no ble#ishes; ble#ishes; a few had one; a very few had two' two' and so on. The average nu#ber was ).* per per door. The distribution distribution of ble#ishes followed followed the Poisson distribution. distribution. @ut of 1)'))) doors painted' painted' about how #any #any would have no ble#ishes= A8 About !')!* /8 About %'4%* 8 About *'))) D8 About *)) Answer: A Difficulty:
!1. A #anufacturer of headache #edicine #edicine clai#s it is 2) percent percent effective within a few #inutes. #inutes. That is' out of every 1)) users 2) get relief within a few #inutes. A group of 1" patients are given the #edicine. +f the clai# is true' what is the probability that 3 have relief within a few #inutes= A8 ).))1 /8 ).1!3 8 ).!!2 D8 )."%1 Answer: D Difficulty: Difficulty:
!". A true5false test consists consists of si$ uestions. uestions. +f you guess the answer to to each uestion' what is the probability of getting getting all si$ uestions uestions correct= A8 ) /8 ).)1! 8 ).)!" D8 )."*) Answer: / Difficulty: Difficulty: Easy oal: &

!%. A far#er who grows genetically engineered corn is e$periencing e$periencing trouble with corn borers. A rando# check of *'))) ears ears revealed the following: #any of the ears contained no borers. ,o#e ears had one borer; a few had two borers; borers; and so on. The distribution distribution of the nu#ber of borers per ear appro$i#ated appro$i#ated the Poisson distribution. distribution. The far#er counted %'*)) borers in the *'))) ears. 9hat is the probability probability that an









!&. A tennis #atch reuires that that a player win three of five sets sets to win the #atch. +f a player wins the first first two sets' what is the probability that the player wins the #atch' assu#ing that each player is eually likely to win each #atch= A8 ).* /8 1G3 or ).1"* ).1"* 8 2G3 or ).32* ).32* D8 annot be co#puted. co#puted. Answer:  Difficulty: Difficulty:
!*. A #achine shop has 1)) drill drill presses and other #achines #achines in constant use. The probability probability that a #achine will beco#e inoperative during during a given day is ).))". During so#e days no #achines are inoperative' but during so#e so#e days' one' two' three or #ore are broken down. 9hat is the probability that fewer than two #achines will be inoperative during a particular day= A8 ).)")) /8 ).1!%2 8 ).3132 D8 ).43"& Answer: D Difficulty: Difficulty:
!!. 9hat is the the following table table called=

A u # b e r o f < e a d s ) 1 " %

P ro b a b ility 1 G3 H % G3 H % G3 H 1 G3 H

A8 Probability distribution /8 u#ulative freuency freuency distribution distribution 8 ,tandard deviation D8 Freuency table Answer: A Difficulty: Easy oal: 1

o f @ u tc o # e ) .1 " * ) .% 2 * ) .% 2 * ) .1 " *











!4. 9hat #ust you know to develop a bino#ial bino#ial probability distribution= distribution= A8 Probability of success success /8 u#ber of trials 8 u#ber of successes D8 a and b only E8 a and c only Answer: D Difficulty: Difficulty: 0ediu# oal: &

2). +n a Poisson distribution distribution the #ean is eual eual to A8 n π Σ ! n /8 8 e 5 $.

! − µ

µ

e

! I D8 E8 6ero. Answer: A

Difficulty: Easy

oal: !

21. +n a Poisson distribution distribution the variance is eual eual to A8 n π . Σ !

/8

n









2*. To construct a bino#ial distribution distribution we need to know the total nu#ber of JJJJJJJJJJJ JJJJJJJJJJJ and the probability of a success. success. Answer: trials Difficulty: Difficulty: Easy oal: &

2!. A probability probability distribution distribution shows the outco#es of an e$peri#ent and the JJJJJJJJJJJJJJJJJJJ JJJJJJJJJJJJJJJJJJJ of each one occurring. Answer: probability Difficulty: Difficulty: Easy oal: 1

22. +n a bino#ial e$peri#ent' e$peri#ent' the probability of a JJJJJJJJJ JJJJJJJJJ re#ains constant. constant. Answer: success or failure Difficulty: Difficulty: Easy oal: &

23. +n a bino#ial e$peri#ent' e$peri#ent' what does the probability probability of a failure eual= JJJJJJJJJJJJJJJJJJJJJJJJJ JJJJJJJJJJJJJJJJJJJJJJJJJJJJJ JJJJ Answer: 1 5 probability of success Difficulty: Difficulty: Easy oal: &

24. A bino#ial bino#ial probability distribution distribution approaches a greater degree of sy##etry as the probability of success re#ains constant and the nu#ber of trials beco#es JJJJJJJJJJJJ Answer: larger or greater Difficulty: Difficulty: 0ediu# oal: &

3). The Poisson distribution distribution or' the law of i#probable events' events' is JJJJJJJJJJJJJJJ skewed. skewed.









3!. +n the JJJJJJJJJJJJJJJJJJJJJJJ JJJJJJJJJJJJJJJJJJJJJJJ distribution distribution the probability of a success is not the sa#e on each trail. Answer: hypergeo#etric hypergeo#etric Difficulty: Difficulty: 0ediu# oal: *

32. For the hypergeo#etric distribution distribution there are JJJJJJJJJJJJJJJJ JJJJJJJJJJJJJJJJ possible outco#es. outco#es. Answer: only " Difficulty: Difficulty: 0ediu# oal: *

33. A rando# rando# variable with a Poisson distribution has one of JJJJJJJ #utually e$clusive values. Answer: two Difficulty: Difficulty: 0ediu# oal: !

34. +n a Poisson distribution each trial is JJJJJJJJJJJJJJJJJ JJJJJJJJJJJJJJJJJJJJ. JJJ. Answer: independent Difficulty: Difficulty: 0ediu# oal: !

4). The arrival of custo#ers custo#ers at a service desk follows follows a Poisson distribution. distribution. +f they arrive at a rate of two every five #inutes' what is the probability that no custo#ers arrive in a five5#inute period= JJJJJJ Answer: ).1%*% Difficulty: Difficulty:
41. The arrival of of custo#ers at a service desk follows follows a Poisson Poisson distribution. distribution. +f they arrive at a rate of four every five #inutes' what is the probability that #ore than four custo#ers arrive in a five #inute period=JJJJJJJJJ period=JJJJJJJJJ









Multiple Choice Questions

-se the following to answer uestions 4!544: DavidKs gasoline station offers & cents off per gallon if the custo#er pays in cash and does not use a credit card. Past evidence indicates indicates that &)L of all custo#ers custo#ers pay in cash. During a one5hour one5hour period twenty5 twenty5 five custo#ers buy gasoline at this station.

4!. 9hat is the probability probability that at least ten ten pay in cash= A8 ).&1! /8 ).*2* 8 ).*3! D8 ).&"* Answer: / Difficulty: Difficulty:
42. 9hat is the probability probability that no #ore than twenty twenty pay in cash= A8 ).) /8 ).1 8 ).4 D8 1.) Answer: D Difficulty: Difficulty: 0ediu# oal: &









1)). 9hat is the probability probability that no wo#an wo#an is selected= A8 1G* /8 1G% 8 "G1* D8 3G1* Answer: / Difficulty: Difficulty:
1)1. 9hat is the probability probability that at least least one wo#an is selected= A8 3G1* /8 %G* 8 "G% D8 %G& Answer:  Difficulty: Difficulty:
Fill-in-the-Blank

1)". 9hat is the probability that that e$actly one wo#an is selected= JJJJJJJJ Answer: 3G1* or ).*%%% Difficulty: Difficulty:
1)%. This is an e$a#ple of what type of probability distribution= distribution= JJJJJJJJJJJ JJJJJJJJJJJ Answer: hypergeo#etric hypergeo#etric Difficulty: Difficulty: 0ediu# oal: !











1)!. 9hat is the probability that that on a rando#ly selected day she will have two #essages= A8 ).))!2 /8 ).))1& 8 ).&") D8 ).)3& Answer: D Difficulty: Difficulty: 0ediu# oal: !

-se the following to answer uestions 1)251)4: A co#pany co#pany is studying the nu#ber of #onthly absences a#ong its 1"* e#ployees. e#ployees. The following probability distribution distribution shows the likelihood that that people were absent )' )' 1' "' %' &' or * days last #onth.

A u # b e r o f d a y s a b s e n t ) 1

P ro b a b ility ) .! ) ) ." )









Fill-in-the-Blank

eference: )!J)* -se the following to answer uestions 11)511%: A co#pany co#pany is studying the nu#ber of daily debit card purchases. +f there were ") purchases and the probability of a debit debit card purchase is ).*' answer answer the following uestions. uestions.

11). @f the ") purchases' what is the e$pected value of the nu#ber of debit card purchases= JJJJJJJJJJJJJJJJJ JJJJJJJJJJJJJJJJJ Answer: 1) purchases Difficulty: Difficulty: Easy oal: &

111. 111. 9hat is the standard deviation deviation of the nu#ber of debit card purchases= JJJJ

chapter06 Discrete Probability Distributions.doc

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