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).

 

·        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.

C(1,6)*C(2,4)/C(3,10)=6*6/120=0.3

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.

Since mean=n*p=36, and standard deviation=sqrt(n*p*(1-p))=4.8,

We can solve for n and p:  n=100, p=0.36

Question 2:                                                                                             Marks: 4+3=7 

a.       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?

Prob(a pack contains more than 1 defective disk)=1-prob(no defective)-prob(only one defective)=1-.98^10-C(1,10)*.98^9*.02=1-.817-.167=.016 (or 1.6%)

b.      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.

Prob(at most 2 accidents)=prob(no accident)+prob(1 accident)+prob(2 accidents)=3^0*e^-3/0! + 3^1*e^-3/1! + 3^2*e^-3/2! = 8.5e^-3=0.423