assignment 3 - probability distribution-1 (1)

8/18/2019 Assignment 3 - Probability Distribution-1 (1)

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Assignment – 3

Probability Distribution

Marks: 5

Guidelines:

1. The assignment MUT be submitted in P!" and PAP!#

$ormat.%. The assignment &hysi'al 'o&y MUT be submitted to

my o('e.3. !a'h grou& )ould submit only *"! assignment by

'learly mentioning the grou& members+ names.,. Please make sure that ea'h member o$ the grou& has

understood the solution be$ore making the

submission. A -i-a-o'e may take &la'e on a random

manner.5. Please submit your original )ork. /o&ying 'ases )ill

be dealt )ith se-erely.0.The deadline $or submission is 1th August %215

be$ore 5:22PM.Please do not hesitate to a&&roa'h me )ith your

doubts.



Assignment 4uestions:

1. Apsychologistdeterminedthatthenumberofsessionsrequiredtoobtainthetrustofanew

patientis1,2,or3.Let x bearandom variableindicatingthenumberofsessionsrequired to

gain the patient’s trust.he following probability function has been proposed.

f ! x " #6

x

for x # 1,2,or3

a. $hatistheprobabilitythatitta%ese&actly2sessionstogainthepatient’strust'b. $hat is the probability that it ta%es at least 2 sessions to gain the patient’s

trust'

2. (ine percent of undergraduate students carry credit card balances greater than

)*,+++. uppose 1+ undergraduate students are selected randomly to be

interviewed about credit card usage.a. $hat is the probability that two of the students will have a balance of )*,+++

or less'b. $hat is the probability that none will have a balance of )*,+++ or less'c. $hat is the probability that at least three will have a balance greater than

)*,+++'

3. he following table gives the number of days in a -+day period during which

automobile accidents occurred in a city. /it 0onstruct a oisson distribution using

this data

(o. of accidents (o. of days

+ 211 1

2 *3 3 1



. /ind the probability that at most - defective bolts will be found in a bo& of 2++

bolts if it is %nown that 2 percent of such bolts are e&pected to be defective.-. A cigar company wants to promote the sales of its cigar brand with a special

advertising campaign. /orty out of every thousand cigars are rolled up in gold foiland randomly mi&ed with the regular cigars. he company offers to trade a new

pac% of cigars for each gold cigar a smo%er finds in a pac%. $hat is the probability that

buyers will find +,1,2,3,4.1+ gold cigars is a single pac% of 1+'5. he income of a group of 1+,+++ persons was found to be normally distributed with

mean # 6s. *-+ per month and standard deviation # 6s. -+. $hat was the lowest

income among the richest 1++'*. 7n an intelligence test administered to 1+++ students, the average score was 2 and

standard deviation was 2. /ind the number of students e&ceeding a score of -+. Also,

find the value of the score e&ceeded by the top 1++ students.

assignment 3 - probability distribution-1 (1)

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