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Gujarat Technological UniversitySummer 2023 Examination

GTU 3130006 Probability and Statistics (PS) Summer 2023 Paper Solution & PDF

B.E. · Computer Engineering · Semester 3 · Subject Code: 3130006
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Total Marks70 MarksExternal theory exam
Passing Marks23 Marks33% minimum cutoff
Exam Duration2.5 Hours2:30 PM – 5:00 PM
Paper Structure5 QuestionsWith internal OR choices
Jump toQ1Q2Q3Q4Q5

Question 1

14 MarksMedium
(a)
A study showed that 65% of managers had some business education and 50% had some engineering education. Furthermore 20% of managers had some business education but no engineering education. What is probability that a manager has some business education, given that he has some engineering education?
3 Marks
(b)
Two computers A and B are to be marketed. A salesman who is assigned the job of finding customers for them has 60% and 40% chances respectively of succeeding in case of Computer A and B. The Computers can be sold independently. Given he was able to sell at least one computer, what is the probability that computer A has been sold?
4 Marks
(c)
In a post office, three clerks are assigned to process incoming mails. The first clerk B1B_1 processes 40%, the second clerk B2B_2 processes 35% and the third clerk B3B_3 processes 25% of the total mails. The first clerk has an error rate of 0.04, the second has an error rate of 0.06 and the third has an error rate of 0.03. A mail selected at random from a day's output is found to have an error. The Post Master wishes to know the probability that the mail was processed by the first, second or third clerk respectively.
7 Marks

Question 2

14 MarksMedium
(a)
The incidence of occupational disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of six workers 4 or more will contract disease?
3 Marks
(b)

On an average one in 400 items is defective. If the items are packed in boxes of 100, what is the probability, that any given box of items will contain:

aNo defective
bLess than two defectives
cOne or more defectives
dMore than three defectives.
4 Marks
(c)

The average daily sales of 500 branch offices was Rs. 150 thousand and the standard deviation Rs. 15 thousand. Assuming the distribution to be normal, indicate how many branches have sales between:

1Rs. 120 thousand and Rs. 145 thousand.
2Rs. 140 thousand and Rs. 165 thousand. [P(0<z<3.3)=0.4772,P(0<z<2)=0.1293,P(0<z<0.67)=0.2486,P(0<z<1)=0.3413][P(0 < z < 3.3) = 0.4772, P(0 < z < 2) = 0.1293, P(0 < z < 0.67) = 0.2486, P(0 < z < 1) = 0.3413]
7 Marks
OR OPTION
(c)
In a Normal distribution 31% of the items are under 45 and 8% are above 64. Find mean and standard deviation of the distribution.
7 Marks

Question 3

14 MarksMedium
(a)
The mean monthly salary paid to all employees in a company is Rs. 1600. The mean monthly salaries paid to technical and non-technical employees are Rs. 1800 and Rs. 1200 respectively. Determine the percentage of technical and non-technical employees of the company.
3 Marks
(b)
Calculate average deviation from mean from the following data:

Sales: 10-20, 20-30, 30-40, 40-50, 50-60 No. of days: 3, 6, 11, 3,

4 Marks
(c)

The median and mode of the following wage distribution are Rs. 33.5 and Rs. 34 respectively. However, three frequencies are missing. Determine their values. Wages: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-70 (Total: 230) Frequency: 4, 16, f0f_0, f1f_1, f2f_2, 6,

7 Marks
OR OPTION
(a)
The following data relate to the sales of 100 companies:

Sales: Below 60, 60-62, 62-64, 64-66, 66-68, 68-70, 70-72 No. of Companies: 12, 18, 25, 30, 10, 3, 2 Calculate the value of modal sales.

3 Marks
(b)
The following data relate to the profits of 1000 companies:

Profits: 100-120, 120-140, 140-160, 160-180, 180-200, 200-220, 220-240 No. of Companies: 17, 53, 199, 194, 327, 208, 2 Calculate the coefficient of skewness and comment on its value.

4 Marks
(c)

The profits earned by 100 companies during 1998-99 are given below. Calculate Q1Q_1, median, D4D_4 and P80P_{80}. Profits: 20-30, 30-40, 40-50, 50-60, 60-70, 70-80, 80-90, 90-100 No. of Companies: 4, 8, 18, 30, 15, 10, 8,

7 Marks

Question 4

14 MarksMedium
(a)
Find correlation coefficient between the sales and expenses from the data given below:

Firm: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Sales: 50, 50, 55, 60, 65, 65, 65, 60, 60, 50 Expense: 11, 13, 14, 16, 16, 15, 15, 14, 13,

3 Marks
(b)

Two housewives, Geeta and Rita, asked to express their preferences for different kinds of detergents, gave the following replies. Detergent: A, B, C, D, E, F, G, H, I, J Geeta: 4, 2, 1, 3, 7, 8, 6, 5, 9, 10 Rita: 4, 1, 2, 3, 8, 7, 5, 6, 9, 10 To what extent the preferences of these two ladies go together?

4 Marks
(c)
Obtain both the regression equations from the data given below:

X: 1, 2, 3, 4, 5, 6, 7, 8, 9 Y: 9, 8, 10, 12, 11, 13, 14, 16, 15 Also calculate the coefficient of correlation.

7 Marks
OR OPTION
(a)
Find the coefficient of correlation by Karl Pearson's method between X and Y and interpret the values.

X: 57, 42, 40, 33, 42, 45, 42, 44, 40, 56, 44, 43 Y: 10, 60, 30, 41, 29, 27, 27, 19, 18, 19, 31, 29

3 Marks
(b)

An examination of eight applicants for a clerical post was taken by a firm. From the marks obtained by the applicants in the accountancy and statistics papers, compute the rank coefficient of correlation. Applicant: A, B, C, D, E, F, G, H Marks in accountancy: 15, 20, 28, 12, 40, 60, 20, 80 Marks in Statistics: 40, 30, 50, 30, 20, 10, 30, 60

4 Marks
(c)
In a partially destroyed laboratory record of an analysis of correlation data the following results are legible:

Variance of X=9X = 9, 8x−10y+66=08x - 10y + 66 = 0, 40x−18y=21440x - 18y = 214. Find on the basis of the above information:

1The mean values of X and Y.
2Coefficient of correlation between X and Y.
3Standard deviation of Y.
7 Marks

Question 5

14 MarksMedium
(a)
The mean lifetime of a sample of 100 light tubes produced by a company is found to be 1580 hours with standard deviation of 90 hours. Test the hypothesis that mean lifetime of the tube produced by the company is 1600 hours. (The critical value of zz at 5% level of significance is ±1.96\pm 1.96).
3 Marks
(b)

Two salesmen A and B are working in a certain district. From a sample survey conducted by the Head office, the following results were obtained. State whether there is any significant difference in the average sales between the two salesmen? Salesman A: No. of sales = 20, Average sales = 170, Standard deviation = 20 Salesman B: No. of sales = 18, Average sales = 205, Standard deviation = 25 The table value of tt at 5% level of significance and 36 df is 1.9.

4 Marks
(c)

Fit a curve y=abxy = ab^x to the following data: x: 2, 3, 4, 5, 6, 8 y: 8.3, 15.4, 33.1, 65.2, 126.4, 146

7 Marks
OR OPTION
(a)
The Prices of shares of a company on the different days in a month were found to be:

66, 65, 69, 70, 69, 71, 70, 63, 64, and 68. Test whether the mean price of the shares in the month is 65. (The table value of tt for 9 degrees of freedom at 5% level of significance is 1.833).

3 Marks
(b)
In random sample of 100 persons taken from village A, 60 are found to be consuming tea. In another sample of 200 persons taken from village B, 100 persons are found to be consuming tea. Do the data reveal significant difference between the two villages as far as the habit of consuming tea is concerned? (The critical value of zz at 5% level of significance is ±1.96\pm 1.96).
4 Marks
(c)
Fit a second degree parabola to the following data:

x: 1, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0 y: 1.1, 1.3, 1.6, 2.0, 2.7, 3.4, 4.1

7 Marks
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About this Examination Paper & Attribution

Official Gujarat Technological University (GTU) examination paper and step-by-step solutions for Probability and Statistics (PS) (Summer 2023, B.E. · Computer Engineering, Sem 3). Features complete 70-mark regular & remedial examination pattern, official marking distribution across all 5 questions, and direct 1-click official PDF download.

Transcribed for student exam preparation from Gujarat Technological University official examination archives. Questions, syllabus guidelines, and curriculum marking schemes remain the intellectual property of Gujarat Technological University.

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