Competitive Examination for the Posts of Provincial Management Services (BPS-17)
Statistics
(i) if all the women sit together
(ii) if all the men refuse to sit together.
(b) A person has purchased 10 out of 1000 tickets sold in a certain raffle. To determine the five prize winners, 5 tickets are to be drawn at random and without replacement. Compute the probability that this person will win an prize.
(c) A class in advance physics is comprised on 10 juniors, 30 seniors and 10 graduate students. The final grades showed that 3 of the juniors 10 of the seniors and 5 of the graduate students received an A for the course. If a student is chosen at random from this class and is found to have earned an A, what is the probability that the student is a junior student? (4+6+10)
i) Percentage of employees requiring more than 4 minutes to complete the task.
ii) The probability that an employee who has just been assigned the task will complete it within 13 minutes.
(c) Number of persons entering a utility store can be assumed to follow a certain distribution. Over a long period of time it has been established that the number of customers that enter the store in an hour is 60 on the average. Find the probability that in a given two-minute interval no customer will enter the store. (6+8+6)
| Car | Kilometers per Liter | |
|---|---|---|
| Radial Tires | Belted Tires | |
| 1 | 4.2 | 4.1 |
| 2 | 4.7 | 4.9 |
| 3 | 6.6 | 6.2 |
| 4 | 7.0 | 6.9 |
| 5 | 6.7 | 6.8 |
| 6 | 4.5 | 4.4 |
| 7 | 5.7 | 5.7 |
| 8 | 6.0 | 5.8 |
| 9 | 7.4 | 6.9 |
(c) Write down short notes on the following: (6+6+8)
(i) Analysis of Variance (ii) p-value (iii) Systematic Sampling
Q.5(a) The following data represent the running times of films produced by two different motion-picture companies:
| Time (minutes) | |||||||
|---|---|---|---|---|---|---|---|
Company 1 |
102 | 86 | 98 | 109 | 92 | ||
Company 2 |
81 | 165 | 97 | 134 | 92 | 87 | 114 |
(b) A geneticist is interested in the proportion of males and females in a population that have a certain minor blood disorder. In a random sample of 100 males, 31 are found to be afflicted, whereas only 24 of 100 females tested appear to have the disorder. Can we conclude at the 0.01 level of significance that the proportion of men in the population afflicted with this blood disorder is significantly greater than the proportion of women afflicted? (12+8)
Q.6(a) Explain the terms “Correlation” and describe the properties of the coefficient of correlation. Also define the coefficient of determination. (6+14)
(b) A study was made by a retail merchant to determine the relation between weekly advertising expenditures (X$) and sales (Y$). The following data were recorded:
Y: 385 400 395 365 475 440 490 420
Q.7(a) Define “Sampling” and discuss the aims of sampling. Also describe the advantages and disadvantages of sampling.
(b) The following table (population) gives the ages (in years) of the five children;
Children: |
A | B | C | D | E |
| Ages (X): | 3 | 5 | 8 | 10 | 11 |
x̄ , where μ x̄
is the mean of the sampling distribution of sample means.
(iv) Find σ 2 x̄ – variance of the sampling distribution of sample means.