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  Assignment No.2 (Course STA301)

Fall 2013 (Total Marks 15)

 

Deadline

Your Assignment must be uploaded/ submitted before or on

February 07 23:59, 2014

STUDENTS ARE STRICTLY DIRECTED TO SUBMIT THEIR ASSIGNMENT BEFORE OR BY DUE DATE. NO ASSIGNMNENT AFTER DUE DATE WILL BE ACCEPTED VIA E.MAIL).

 

Rules for Marking

It should be clear that your Assignment will not get any credit IF:

  • The Assignment submitted, via email, after due date.
  • The submitted Assignment is not found as MS Word document file.
  • There will be unnecessary, extra or irrelevant material.
  • The Statistical notations/symbols are not well-written i.e., without using MathType software.
  • The Assignment will be copied from handouts, internet or from any other student’s file. Copied material (from handouts, any book or by any website) will be awarded ZERO MARKS. It is PLAGIARISM and an Academic Crime.
  • The medium of the course is English. Assignment in Urdu or Roman languages will not be accepted.
  • Assignment means Comprehensive yet precise accurate details about the given topic quoting different sources (books/articles/websites etc.). Do not rely only on handouts. You can take data/information from different authentic sources (like books, magazines, website etc) BUT express/organize all the collected material in YOUR OWN WORDS. Only then you will get good marks.

 

 

Objective(s) of this Assignment:

 

This assignment will strengthen the basic idea about the concept of the following distributions:

  • Poisson distribution
  • Binomial distribution
  • Hypergeometric distribution

 

 

 

 

 

 

 

 

Assignment No: 2 (Lessons 27 – 30)

Question 1:                                                                                             Marks: 4+4=8

a)     A batch of 10 gaskets contains 4 defective gaskets. If we draw samples of size 3 without replacement, from the batch of 10, find the probability that a sample contains 2 defective gaskets.

b)     In a binomial distribution, the mean and the standard deviation were found to be 36 and 4.8 respectively. Find the parameters of binomial distribution.

 

Question 2:                                                                                             Marks: 4+3=7 

  1. It is known that the computer disks produced by a company are defective with probability 0.02 independently of each other.  Disks are sold in packs of 10. A money back guarantee is offered if a pack contains more than 1 defective disk. What is the probability of sales result in the customers getting their money back?
  2. The average number of accidents occurring in an industrial plant during a day is 3. Assuming Poisson distribution for the number of accidents (X) during a day, compute probability that at most two accidents occur in a day.

 

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Discuss here Assignment 2

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Our main purpose here discussion not just Solution

We are here with you hands in hands to facilitate your learning and do not appreciate the idea of copying or replicating solutions.

Question 1:                                                                                             Marks: 4+4=8

a)     A batch of 10 gaskets contains 4 defective gaskets. If we draw samples of size 3 without replacement, from the batch of 10, find the probability that a sample contains 2 defective gaskets.

Solution

A batch of 10 rocker cover gaskets contains 4 defective gaskets. If we draw samples
of size 3 without replacement, from the batch of 10, find the probability
that a sample contains 2 defective gaskets.

It is possible to derive formulae for the mean and variance of the Hypergeometric distribution.
However, the calculations are more difficult than their Binomial counterparts, so we will simple
state the results.

Question 2:                                                                                             Marks: 4

  1. It is known that the computer disks produced by a company are defective with probability 0.02 independently of each other.  Disks are sold in packs of 10. A money back guarantee is offered if a pack contains more than 1 defective disk. What is the probability of sales result in the customers getting their money back?

Solution:

p of a defective disk is equal to .02
sell disks in a pack of 10.
probability of more than 1 disk being defective is equal to 1 minus the probability that 0 or 1 are defective. 

probability that 0 out of the 10 pack are defective is equal to 10c0 * .02^0 * .98^10 which is equal to .817073 

probability that 1 out of the 10 pack are defective is equal to 10c1 * .02^1 * .98^9 which is equal to .166749 

probability that 0 or 1 out of the 10 pack are defective is equal to .817073 + .166749 which is equal to .983822 

the probability that more than 1 are defective is therefore equal to 1 minus .983822 which is equal to .016177. 

Looks like they will have to give the money back 1.6% of the time. 

the complete table of probabilities is shown below.

x is equal to the probability of having a defective disk.
ncx is equal to the number of possible combinations of 10 things taken x at a time.
p(x) is the probability of getting one defective disk.
p(1-x) is the probability of not getting one defective disk.
the complete formula is:
the probability of getting x defective disks out of 10 is equal to ncx * p(x)^x * p(1-x)^(n-x).
for example, the probability of getting 3 defective disks out of 10 is equal to:
10C3 * (.02)^3 * (.98)^7 which is equal to 120 * (.02)^3 * (.98)^7 which is equal to 8.33401 * 10^-4.
that's in scientific notation.
in standard decimal notation it is equal to .000833401.

aslam o alikum!

is this correct?

In 3rd equetion after taking SD  

npq =23.04

36q=23.04

     q=23.04/36

      q=0.64

Rosali chek it again

right but tell is this fine solution or the 1 given by admin??????

question # 2 ka b part kasa karna ha plzzzzzzzzzzzzzzzz helppppppppp     anybody 

 Muhammad Aslam  ap ke calculation wrong ha 

friends 1st question mein jo aek formula 

P(X=r) = mcr x N-McN-R / NCN kahan sy lea ha

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