Assignment Problems - Date of submission 10 Sept 2012., (total seven problems)

1. In a recent nationwide poll conducted in India, the prob that the people are right opinionated is 0.55, left opinionated is 0.30 and middle of the road for the balance 0.15. Assuming that these probabilities are accurate, answer the following questions pertaining to a randomly chosen group of 15 Indians.
a. what is the prob that four of them are right opinionated
b. prob that none are left opinionated
c. prob hat three are middle of the road
d. prob that at least eight are left opinionated

2. Find for a binomial distribution with n=10, p=.4,
a. prob (r = 5)
b. prob (r > 6)
c. prob (r < 8)
d. prob (r >= 7)

3. Given that lamda = 6.1 for a Poisson Distribution, find
a. prob (x <= 3)
b. prob (x >= 2)
c. prob (x =6)
d. prob (1 <=  x <= 4)

4. A R Rehman is very much concerned about people coughing before his performances. On his latest concert he found that on an average 8 coughs occur before start of the performance. Rehman has told his manager that if he hears more than 6 coughs before the start of the concert to be held on 20 Sept at Alliance central campus, he will not perform. What is the prob that he will perform on 20 Sept.?

5. MRF is coming out with a latest tyre and they do not know what is the average amount of tread life. But they know that the average life is normally distributed with standard deviation of 200 kms.
a. If the company samples 100 tyres, and records their tread life, what is the probability that the sample mean is between the true mean and 500 kms over the true mean.
b. how large a sample must be taken to be 95% sure, the sample mean will be within 200 kms of the true mean.

6. For a population of size N=80, with a mean of 8.2 and a std dev of 2.1, find the standard error of the mean for the following sample sizes.
a. n = 16
b. n = 25
c. n = 36

7. After the release of Raone, the distributors have come to realise the film ran for 74 days in each of the major cities and towns in the country with a corr standard deviation of 10 days. The Producer however is interested in finding how the movie fared in South India in comparison to all other Indian cities. He randomly chose 75 cities and towns and found that the movie ran an average of 78 days.
a. State appropriate hypothesis for testing whether there was a significant difference in the length of the picture's run between theatres in the South and all India.
b. At a one percent significance level test these hypothesis.

Partial Distributions Hypothesis testing ppt and problems ..

PPT on Sample Distributions and problems ..

Hypothesis Testing and problems ..

ge..

Simulation tool for Central Limit Theorem .. www.onlinestatbook.com

www.onlinestatbook.com   courtesy Rice University ..

Here is the simulation link for the Central Limit Theorem demo ..

Hope you enjoy this demo well and have got your basics clear ..

ge..

Probability Distribution problems

Here is the link of the problems related to Probability Distributions discussed in the class on 2 Sept 2012.

george ..

Google Drive - Normal Dist Demo spreadsheet ..

Check out the Normal Distribution demo spreadsheet  here ..

ge..

Google Drive - Binomial Dist Spreadsheet ..

Check out the Binomial Distribution spreadsheet - Google Drive here..

ge..