1. A salesman has the following record of sales during three months for three items B and which have different rates of commission

Month
Sale of Units Total Commission
A B C drawn (in
Jan 90 100 20 800
Feb 130 50 40 900
Mar 60 100 30 850

Find out the rates of commission on items B and C.

2. The following results were obtained on the basis of runs scored by two players A and B in 10 matches. Who is a more consistent player?

Player A Player B
Average runs 44.30 62.70
Standard deviation 4.21 9.83

3. In a sample of 1,000 cases, the mean score of a certain test is 14 and standard deviation is 2.5. Assuming normality find:

How many candidates score between 12 and 15

What is the probability that a candidate selected at random will score above 20


4. What is time series analysis? Decompose a time series into its various components and describe them.

5. In a locality of 18,000 families, a sample of 840 families was selected at random. Of the 840 families, 210 had a weekly income of RS 500 or less. Estimate the number of families having weekly income of RS 500 or less in the population at 99.73% confidence level.

6. Write short notes on any three of the following:

Absolute value function

Skewness

Baye's Theorem

Multistage sampling

Delphi

7. What is a random variable? How is it used to define a probability distribution? Make the probability distribution of "Number of Heads" in a toss of three coins.

8. A HR manager is interested in trying to determine whether absenteeism is uniformly distributed over the week days? His record for the past year show this sample distribution


Day of the week Mon Tue Wed Thu Fri

No. of Absentees 66 57 54 48 75

Test whether the absense is uniformly distributed over the week? (Given tabulated value of test statistic at 0.05 is 9.49)