What is the exam pattern and passing mark for GTU Probability and Statistics (3130006)?

The GTU theory examination carries 70 total marks with a duration of 2.5 Hours. Minimum passing criteria is 23 marks (33%). The paper consists of 5 main questions with official marking breakdown and internal choices.

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Gujarat Technological UniversitySummer 2023 examination

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

B.E. · Computer Engineering · Semester 3 · Subject code 3130006

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Total: 70 marks
To pass: 23 marks (33%)
Duration: 2.5 Hours 2:30 PM – 5:00 PM
Questions: 5 with internal choice

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4 of 25 questions on this paper were also asked in other years. 11 more are types of question GTU sets again with new data. Each is marked below with the years it appeared.See all 33 repeated 3130006 questions, most asked first

Q.1

14 Marks

(a)

3 marks

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?

(b)

4 marks

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?

(c)

7 marksSame type asked in 6 of 7 papers

In a post office, three clerks are assigned to process incoming mails. The first clerk

B_1

processes 40%, the second clerk

B_2

processes 35% and the third clerk

B_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.

Also asked in Winter 2025 Q1b, Summer 2025 Q2c, Winter 2024 Q2c, Summer 2024 Q1c, Winter 2023 Q1c

Q.2

14 Marks

(a)

3 marksAsked in 2 of 7 papers

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?

Also asked in Winter 2025 Q4b

(b)

4 marksSame type asked in 4 of 7 papers

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.

Also asked in Winter 2025 Q4a OR, Summer 2025 Q2c OR, Winter 2023 Q3a

(c)

7 marksSame type asked in 4 of 7 papers

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]

Also asked in Summer 2025 Q5c, Winter 2024 Q5c, Summer 2024 Q5c

(c)

7 marksAsked in 3 of 7 papers

In a Normal distribution 31% of the items are under 45 and 8% are above 64. Find mean and standard deviation of the distribution.

Also asked in Winter 2025 Q4b OR, Winter 2023 Q3b OR

Q.3

14 Marks

(a)

3 marks

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.

(b)

4 marks

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,

(c)

7 marksSame type asked in 2 of 7 papers

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, $f_0$ , $f_1$ , $f_2$ , 6,

Also asked in Summer 2026 Q3b OR

(a)

3 marks

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.

(b)

4 marks

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.

(c)

7 marks

The profits earned by 100 companies during 1998-99 are given below. Calculate $Q_1$ , median, $D_4$ and $P_{80}$ . 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,

Q.4

14 Marks

(a)

3 marksSame type asked in 6 of 7 papers

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,

Also asked in Winter 2025 Q3c, Summer 2025 Q3c, Winter 2024 Q3c, Summer 2024 Q3c, Winter 2023 Q4c OR

(b)

4 marksSame type asked in 5 of 7 papers

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?

Also asked in Summer 2026 Q3a OR, Winter 2025 Q3b OR, Summer 2025 Q3b, Winter 2023 Q4c

(c)

7 marks

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.

(a)

3 marksSame type asked in 6 of 7 papers

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

Also asked in Winter 2025 Q3c, Summer 2025 Q3c, Winter 2024 Q3c, Summer 2024 Q3c, Winter 2023 Q4c OR

(b)

4 marks

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

(c)

7 marksAsked in 2 of 7 papers

In a partially destroyed laboratory record of an analysis of correlation data the following results are legible:

Variance of $X = 9$ , $8x - 10y + 66 = 0$ , $40x - 18y = 214$ . 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.

Also asked in Winter 2023 Q4b

Q.5

14 Marks

(a)

3 marksSame type asked in 3 of 7 papers

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

z

at 5% level of significance is

\pm 1.96

Also asked in Summer 2026 Q5b OR, Winter 2025 Q5a

(b)

4 marks

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 $t$ at 5% level of significance and 36 df is 1.9.

(c)

7 marksAsked in 2 of 7 papers

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

Also asked in Winter 2023 Q2c OR

(a)

3 marksSame type asked in 4 of 7 papers

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 $t$ for 9 degrees of freedom at 5% level of significance is 1.833).

Also asked in Summer 2026 Q5a, Winter 2024 Q4a OR, Winter 2023 Q5a OR

(b)

4 marksSame type asked in 4 of 7 papers

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

z

at 5% level of significance is

\pm 1.96

Also asked in Summer 2026 Q4b OR, Winter 2025 Q5a OR, Winter 2024 Q4c

(c)

7 marksSame type asked in 5 of 7 papers

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

Also asked in Winter 2025 Q2c OR, Summer 2025 Q1c, Winter 2024 Q5c OR, Winter 2023 Q2c

More Probability and Statistics papers

Questions repeat across sessions. Working through two or three papers shows you which topics GTU asks most.

Summer 202670 marks · 5 questions · Solved

Winter 202570 marks · 5 questions

Summer 202570 marks · 5 questions

Winter 202470 marks · 5 questions

Other Semester 3 subjects

BE Computer

130001

Mathematics-III

3130004

Effective Technical Communication

3130702

Data Structures

3130703

DATABASE MANAGEMENT SYSTEM

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About this paper

Official Gujarat Technological University (GTU) examination paper 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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