1. The distribution of Intelligence Quotient (I.Q.) scores measured for 100 students in a test is as follows:
I.Q.*

4050

5060

6070

7080

8090

90100

Number of Students

10

20

20

15

15

20

* The data is recorded with origin as 40, i.e. students with I.Q. between 80 and 90 are included in the first interval. The intervals included the upper class value but not the lower.
Find: Arithmetic Mean, Median, First and Third Quartiles, 90^{th} percentile and 6^{th} Decile.
2. A candidate is selected for interview for 3 posts. For the first post, there are 3 candidates, for the second, 4 and for the third post there are 2 candidates. What is the probability that the candidate is selected for at least one post?
3. The lifetimes of a colour TV picture tube is normally distributed, with a mean of 8 yrs and a standard deviation of 2 years.
(i) What is the probability that a picture tube will last more than 10 yrs?
(ii) If the firm guarantees the picture tube for 4 yrs, what percentage of the tubes sold will have to be replaced?
4. Make a list of formulae for all confidence intervals, sample size determination and tests of hypothesis that you have read in your study material.
5. What is a time – series? Discuss four components of a time – series. Why is it generally assumed that the impact of these components is multiplicative?