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Q.1. The average monthly sales of 5000 firms are normally distributed. Its mean and standard deviation are Rs.36,000 and Rs. 10,000 respectively.
Find
i) the number of firms having sales over Rs.40,000
ii) the percentage of firms having sales between Rs.38,500 and Rs.41,000
iii) The number of firms having sales between Rs. 30,000 and Rs. 40,000.
The relevant extract of the area table( under the normal curve)
| Z |
0.25 |
0.40 |
0.5 |
0.6 |
| Area |
0.0987 |
0.1554 |
0.1915 |
0.2257 |
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Q.1.a) A sub-committee of 6 members is to be formed out of a group consisting of 7 men and 4 women. Calculate the probability that the sub-committee will consist of
i) exactly 2 women
ii)at least 2 women
b) Find the probability in each of them following events:
i) At least one head appears in two tosses of a fair coin
ii) The sum 8 appears in a single toss of a pair of fair dice
iii) An ace, a king, a queen or ten of hearts appears in drawing a single card from a deck of 52 playing cards. |
Q.1. A Company has derived three training methods to train its workers. It is keen to know which of these three training methods would lead to greatest productivity after training. Given below are productivity measures for individual workers trained by each method.
Find out whether the three training methods lead to different levels of productivity at the 0.05 level of significance(2,18)at 0.05 level of significance is 3.55.
| Method 1 |
Method 2 |
Method 3 |
| 30 |
55 |
42 |
| 40 |
46 |
38 |
| 45 |
37 |
49 |
| 38 |
43 |
40 |
| 48 |
52 |
55 |
| 55 |
42 |
36 |
| 52 |
40 |
41 |
Q.1An investigation into the demand for television sets in 7 towns has resulted in the following data:
i) Fit a linear regression of Y on X and
ii) Estimate the demand of T.V. sets of
20 lakh
32 lakh.
| Town |
Population in lakhs (X) |
No. of TV sets demanded ‘000 (Y) |
| A |
11 |
15 |
| B |
14 |
27 |
| C |
14 |
27 |
| D |
17 |
30 |
| E |
17 |
34 |
| F |
21 |
38 |
| G |
25 |
46 |
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Q.1.A Company manufactures different types of electrical appliances. It has been using radio for advertising its products. The following table shows amounts of radio time (X, in minutes) and the number of electrical appliances sold (Y) over the last six weeks.
Calculate the coefficient of correlation between the two series.
| X |
y |
| 25 |
16 |
| 18 |
11 |
| 32 |
20 |
| 21 |
15 |
| 35 |
26 |
| 29 |
28 |
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Q.1.An owner of the press claims that the life of its largest web press is 14,500 hours with a standard deviation of 2,100 hours. From a sample of 25 presses, the company finds a sample mean of 13,000 hours. Do you think that the average life of the presses is different from 14,500 hours as claimed by the company? Verify it at 0.01 level of significance.
t value for 24 degrees of freedom at 1% level of significance is -2.492.
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Q.1.Suppose a prospective buyer tests bursting pressure of sample of polythene bags received from two manufacturers A and B .The tests reveal the following results:
| Bursting Pressure (lbs) |
No. of Bags |
No. of Bags |
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A |
B |
| 5 – 10 |
2 |
9 |
| 10-15 |
9 |
15 |
| 15-20 |
29 |
30 |
| 20-25 |
54 |
32 |
| 25-30 |
6 |
14 |
Which manufacturer’s bags, judging from these two samples, have the higher average bursting pressure? Which of them is more uniform in bursting pressure? |
Q.1.a)Calculate the mean, median and mode for the following set of numbers:
3,5,2,6,5,9,5,2, 8 and 6
b)The following data relate to monthly income and expenditure under different heads for two families.
Show these data by a suitable diagram.
| Item of Expenditure |
Family A (Monthly income Rs.12,000) |
Family B (Monthly income Rs. 16,000) |
| Food |
4,000 |
4,800 |
| Clothing |
2,500 |
3,000 |
| Rent |
3,000 |
4,000 |
| Education |
1,500 |
2,500 |
| Fuel and Lighting |
400 |
800 |
| Others |
600 |
900 |
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Q.1. Prepare a frequency distribution for the following data giving the heights of 30 children. Also calculate less than and more than cumulative frequencies. Take class intervals as 120-125,125-130
121 133 137 127 132 134
131 126 124 135 139 127
137 130 133 144 131 132
127 140 126 134 128 143
123 125 136 129 141 137 |
Q.10. Lives of two models of refrigerators in a survey was found to be:
| Life (No. of years) |
No. Of Refrigerators |
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MODEL A |
MODEL B |
| 0 -2 |
5 |
2 |
| 2-4 |
16 |
7 |
| 4-6 |
13 |
12 |
| 6-8 |
7 |
19 |
| 8-10 |
5 |
9 |
| 10-12 |
4 |
1 |
What is the average life of each model of these refrigerators? |
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