(b) A coal-fired power plant is considering two different systems for pollution abatement. The first system has reduced the emission of pollutants to acceptable levels 68 percent of the time, as determined from 200 air samples. The second, more expensive system has reduced the emission of pollutants to acceptable levels 76 percent of the time, as determine from 250 air samples. If the expensive system is significantly more effective than the inexpensive system in reducing pollutants to acceptable levels, then the management of the power plant will install the expensive system. To decide that

(i) State null and alternative hypotheses

(ii) Name the test which is suitable in this situation and why?

(iii)Calculate the value of test statistic and critical value.

(iv)Which system will be installed if management uses a significance level 0.01 in making decision?

The production department for a company requires 3600 kg of raw material for manufacturing a particular item per year. It has been estimated that the cost of placing an order is Rs 36 and the cost of carrying inventory is 25 percent of the investment in the inventories. The price is Rs10 per kg. The purchase manager wishes to determine an ordering policy for raw material

i) What is the probability that the mean length of service times is more than and equal to 12 minutes.
ii) Find the 99% confidence interval for the standard deviation of the mean length of service times.

If X is a continuous random variable then

A fair die is tossed. If the resulting number is even, you add 1 to your score and get that many rupees. If the resulting number is odd, you add 2 to your score and get that many rupees. If X denotes the random variable counting your gain in rupees, then write probability distribution of X.

Twenty Five successive observations on a stationary time series are given as follows: 30, 33, 32, 27, 25, 28, 29, 31, 35, 34, 38, 31, 23, 24, 34, 36, 29, 32, 38, 27, 22, 29, 20, 40, 37. Calculate r₁, r₂, ....., r₁₀ and plot the correlogram.

A solicitors’ firm employs typists on hourly price-rate basis for their daily work. There are five typists and their charges and speed are different. According to an earlier understanding only one job is given to one typist and the typist is paid for a full hour even if he works for a fraction of an hour. Find the least cost allocation for the following data: