Quiz - II Solution

Business Statistics Quiz 2 Maximum Marks: 20

Maximum Duration:

20

Minutes

1. Which one of these these variab variables les is is a continuo continuous us random random variab variable? le? a. The number of women taller than ! inches in a random sam"le of # women.  b. The number of correct $uesses $uesses on a multi"le choice choice test. c. The time it ta%es a randoml& selected student to com"lete an e'am. d. The number of tattoos a randoml& selected "erson has. 2. (ulse rates rates of adult adult men are a""ro'im a""ro'imatel& atel& normal normal with with a mean of )0 and a standard standard deviat deviation ion of  !. Which choice correctl& describes how to find the "ro"ortion of men that have a "ulse rate $reater than )!? a. *ind the area to the ri$ht of z +1 under a standard normal curve.  b. *ind the area to the left of z + ,1 under under a standard normal curve. curve. c. *ind the area to the left of z + 1 under a standard normal curve. d. *ind the area between z + ,1 and z + 1 under a standard normal curve. -. What is the the median median of of the standard standard normal normal distr distribut ibution? ion? a.  b. c. d.

0 1 0.# This This can canno nott be dete determ rmin ined ed

. /n the te'tile te'tile industr& industr& a manufacturer manufacturer is interested interested in the the number of blemishes blemishes or flaws flaws occurrin$ occurrin$ in each 100 feet of material. The "robabilit& distribution that has the $reatest chance of a""l&in$ to this situation is the a. normal distribution  b. binomial distribution distribution c. (oisson distribution d. uniform distribution #. Which of the follow followin$ in$ is not not a "ro"ert& "ro"ert& of a binomi binomial al e'"erimen e'"eriment? t? a. the e'"eriment consists of a seuence of n identical trials  b. each outcome can be referred to as a success success or a failure c. the "robabilities of the two outcomes can chan$e from one trial to the ne't d. the trials are inde"endent . Which one of these these variab variables les is is a binomia binomiall random random variable variable?? a. time it ta%es ta%es a randoml& randoml& selected selected student student to com"lete com"lete a multi" multi"le le choice choice e'am  b. number of te'tboo%s a randoml& randoml& selected student student bou$ht this term c. number number of women women taller taller than than ! inches inches in a random random sam"le sam"le of # women women d. num number ber of 3s 3s a random randoml& l& selec selected ted "ers "erson on owns owns

). Su""ose 04 of a herd of cattle is infected with a "articular disease. 5et 6 + the number of non7 diseased cattle in a sam"le of size #. The distribution of 6 is a. binomial with n + # and " + 0.  b. binomial with n + # and " + 0. c. binomial with n + # and " + 0.# d. (oisson with 8 + .

( )

 P   x

!. onsider the followin$ "robabilit& distribution9 *ind the mean of the random variable '. a. # b. -# c. 0.21

#: =

 x:

(#

−

( 0.) ) ( 0.-) #  x

 x

):

−

x

  x

=

0 1 ... #

d. -.#

;. *or a binomial distribution a. n must assume a number between 1 and 20. c. There must be at least - "ossible outcomes

b. ( must be multi"le of 0.10 d.
10. Which of the followin$ is not true concernin$ discrete "robabilit& distribution? a. The "robabilit& of an& s"ecific value is between 0 and 1 inclusive.  b. The mean of the distribution is between the smallest and lar$est value of the discrete random variable. c. The sum of all "robabilities is 1. d. The standard deviation of the distribution is between 71 and 1. 11. = business evaluates a "ro"osed venture as follows. /t stands to ma%e a "rofit of >10000 with  "robabilit& -20 to ma%e "rofit of >#000 with "robabilit& ;20 to brea% even with "robabilit& 1 and to lose >#000 with "robabilit& -20. The e'"ected "rofit in dollars is9 i.e. a. 1#00

b. 0

c. 71#00

d. -000

12. The distribution of the number of "eo"le lo$$in$ into a lar$e com"uter networ% durin$ a five second "eriod is  a. binomial

b.
c. (oisson

d.
1-. = die is thrown at random. What is the e'"ectation of the number on it9 a. -.) b -.1 c. -.# d. -.! 1. Tina@s score on her midterm e'am was at the #0th "ercentile. The $rades were normall& distributed. The e'am avera$e was )! and the standard deviation was . What was Tina@s score on the e'am? a. ;0 b. #0 c. ! d. )! 1#. /f the time between customer arrivals at a ban% is a random variable A which follows a normal distribution with mean of )# seconds and a variance of ; minutes then a""ro'imatel& ;#4 of the times between arrivals are between9 a.  seconds and ! seconds  b. #) seconds and ;- seconds c. ; seconds and !1 seconds

d. )2 seconds and )! seconds e. ! seconds and 102 seconds

1. The followin$ table $ives the "robabilit& distribution of the number of "eo"le in cars travellin$ alon$ a certain freewa&.  p

(rC P  +  pD

1

2

-

-

0.#

0.-#

0.0#

0.1#

= toll of >#.00 is char$ed on cars which carr& onl& the driverE otherwise the toll "er car is onl& >1.#0. The e'"ected toll char$e "er car is eual to9 a. >1.0# b. >1.10 c. >1.# d. >-.0)# 1). (robabilit& distribution of discrete random variable is classified as a.  b. c. d.

"robabilit& mass function "osterior mass function interior mass function continuous mass function

1!. Mean of binomial "robabilit& distribution is !#). and "robabilit& is 4 then number of values of binomial distribution a. 100

b. 1-0

c. 120

d. 110

1;. /n normal distribution normal curve becomes more wider and more flatter because of  a.  b. c. d.

small value of mean lar$e value of mean lar$e value of standard deviation small value of standard deviation

20. /f mean of a random variable A which follows a (oisson distribution is 2# then standard deviation of A is a.  b. c. d.

2# # 2# This cannot be determined