R09 Code No: 09A30302 JAWAHARLAL NEHRU ...liet-clmc.yolasite.com/resources/Probability_and...normally distributed with an average life of 2040 hours and S.D of 40 hrs. Estimate the

Code No: 09A30302

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY, HYDERABAD

B.Tech II Year I Semester Examinations, May/June-2013

Probability and Statistics (Common to ME, CSE, MCT, AME, MIE)

Time: 3 hours Max. Marks: 75

Answer any five questions

All questions carry equal marks

- - -

1.a) There are ten chips numbered 1 to 10. Two chip are drawn. Find the probability

that the sum is greater than 4.

i) When the selection is with replacement

ii) When the selection is without replacement.

b) A sample of 4 items is selected at random from a box containing 12 items of

which 5 are defective find the expected number of defective items. [15]

2.a) The probability that a man hits a target is 1

2. He fires 6 times. Find the probability

that he hits the target (i) Exactly 2 times (ii) More than 4 times (iii) At least once.

b) In a test on electrical bulbs, it was found that the life of a particular make was

normally distributed with an average life of 2040 hours and S.D of 40 hrs.

Estimate the number of bulbs likely to burn for more than 2140. [15]

3.a) The dean of college wants to use the mean of a random sample to estimate the

average amount of time students take to get from one class to the next and she

wants to be able to assert with 99% confidence that the error is at most 0.25

minute. If it can be presumed from experience that 1.40 minutes. How large a

sample will she have to take?

b) It is claimed that a random sample of 100 tyres with a mean life of 15269 is

drawn uom a population of tyres which has a mean life of 15200 km and a

standard deviation of 1248 km. Test the validity of this claim. [15]

4.a) A manufacturer claimed that at least 95% of the equipment which he supplied to a

factory conformed to specifications. An examination of a sample of 200 pieces of

equipments revealed that 180 were faulty. Test his claim at a significant level of

0.05

b) A study shows that 16 of 200 Tractors produced on one assembly line required

extensive adjustments before they could be shipped, while the same was true for

14 of 400 tractors produced on another assembly line. At the 0.01 level of

significance, does this support the claim that the second production line does

superior work. [15]

5. Two horses A and B were tested according to the time (in seconds) to run a

particular track with the following results.

Horse A 28 30 32 33 35 29 34

Horse B 29 30 30 24 27 29 37

Test whether the two horses have the same running capacity. [15]

R09


wants to be able to assert with 99% c

minute. If it can be presumed from experience that



drawn uom a population of tyres which

standard deviation of 1248 km. Test the validity of

4.a) A manufacturer claimed that at least 95%

b) In a test on electrical bulbs, it was

ally distributed with an averag





umed from experience that


wants to be able to assert with 99% c

minute. If it can be presumed from experience that





4.a) A manufacturer claimed that at least 95%

b) In a test on electrical bulbs, it was found that the life of a particular make was






umed from experience that minute. If it can be presumed from experience that









At the 0.01 level of


At the 0.01 level of


on another assembly line. At the 0.01 level of


on another assembly line.


on another assembly line.


tractors produced


400 tractors produced


14 of 400

produced on one assembly line required produced on one assembly line required produced on one assembly line required produced on one assembly line required b) A study shows that 16 of 200 Tractorsb) A study shows that 16 of 200 Tractorsb) A study shows that 16 of 200 Tractorsb) A study shows that 16 of 200 Tractorsb) A study shows that 16 of 200 Tractors

amination of a sample of 200 pieces of

significant level of


significant level of


Test his claim at a


Test his claim at a

factory conformed to specifications. An ex

equipments revealed that 180 were faulty.







ich he supplied to a ich he supplied to a of the equipment wh of the equipment wh4.a) A manufacturer claimed that at least 95%4.a) A manufacturer claimed that at least 95%4.a) A manufacturer claimed that at least 95%4.a) A manufacturer claimed that at least 95%4.a) A manufacturer claimed that at least 95%

this claim. [15] this claim. [15] this claim. [15] this claim. [15] this claim. [15] standard deviation of 1248 km. Test the validity of






standard deviation of 1248 km. Test the validity of standard deviation of 1248 km. Test the validity of




standard deviation of 1248 km. Test the validity of standard deviation of 1248 km. Test the validity of standard deviation of 1248 km. Test the validity of

drawn uom a population of tyres which drawn uom a population of tyres which

b) It is claimed that a random sample of 100 tyres with a mean life of 15269 is b) It is claimed that a random sample of 100 tyres with a mean life of 15269 is b) It is claimed that a random sample of 100 tyres with a mean life of 15269 is b) It is claimed that a random sample of 100 tyres with a mean life of 15269 is b) It is claimed that a random sample of 100 tyres with a mean life of 15269 is






b) It is claimed that a random sample of 100 tyres with a mean life of 15269 is b) It is claimed that a random sample of 100 tyres with a mean life of 15269 is


b) It is claimed that a random sample of 100 tyres with a mean life of 15269 is b) It is claimed that a random sample of 100 tyres with a mean life of 15269 is

minutes. How large a minutes. How large a 1.40umed from experience that umed from experience that umed from experience that umed from experience that umed from experience that minute. If it can be presminute. If it can be presumed from experience that

mean of a random sample to estimate the







average amount of time students take to get from one class to the next and she average amount of time students take to get from one class to the next and she average amount of time students take to get from one class to the next and she

3.a) The dean of college wants to use the

average amount of time students take to get from one class to the next and she average amount of time students take to get from one class to the next and she average amount of time students take to get from one class to the next and she








to burn for more than 2140. [15] to burn for more than 2140. [15] to burn for more than 2140. [15] to burn for more than 2140. [15] Estimate the number of bulbs likely Estimate the number of bulbs likely Estimate the number of bulbs likely Estimate the number of bulbs likely

found that the life of a particular make was

e life of 2040 hours and S.D of 40 hrs.








ally distributed with an average life of 2040 hours and S.D of 40 hrs.


ally distributed with an averagally distributed with an averag




normally distributed with an averag


More than 4 times (iii) At least once. More than 4 times (iii) At least once. More than 4 times (iii) At least once. More than 4 times (iii) At least once. that he hits the target (i) Exactly 2 times (ii) that he hits the target (i) Exactly 2 times (ii) that he hits the target (i) Exactly 2 times (ii) that he hits the target (i) Exactly 2 times (ii)

number of defective items. [15] number of defective items. [15] number of defective items. [15] which 5 are defective find the expectedwhich 5 are defective find the expectedwhich 5 are defective find the expectedwhich 5 are defective find the expected

b) A sample of 4 items is selected at random from a box containing 12 items of b) A sample of 4 items is selected at random from a box containing 12 items of b) A sample of 4 items is selected at random from a box containing 12 items of b) A sample of 4 items is selected at random from a box containing 12 items of

is without replacement.


is without replacement.


ii) When the selection


ii) When the selection

b) A sample of 4 items is selected at random from a box containing 12 items of b) A sample of 4 items is selected at random from a box containing 12 items of




i) When the selection is with replacement i) When the selection is with replacement



Two chip are drawn. Find the probability Two chip are drawn. Find the probability Two chip are drawn. Find the probability Two chip are drawn. Find the probability 1.a) There are ten chips numbered 1 to 10. Two chip are drawn. Find the probability 1.a) There are ten chips numbered 1 to 11.a) There are ten chips numbered 1 to 11.a) There are ten chips numbered 1 to 11.a) There are ten chips numbered 1 to 1

All questions carry equal marks All questions carry equal marks All questions carry equal marks

Time: 3 hours Max. Marks: 75 Time: 3 hours Max. Marks: 75 Time: 3 hours Max. Marks: 75 Time: 3 hours Max. Marks: 75






Time: 3 hours Max. Marks: 75 Time: 3 hours Max. Marks: 75 Time: 3 hours Max. Marks: 75



Probability and Statistics (Common to ME, CSE, MCT, AME, MIE) (Common to ME, CSE, MCT, AME, MIE)

AWAHARLAL NEHRU TECHNOLAWAHARLAL NEHRU TECHNOL JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY, HYDERABAD OGICAL UNIVERSITY, HYDERABAD OGICAL UNIVERSITY, HYDERABAD OGICAL UNIVERSITY, HYDERABAD AWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY, HYDERABAD

09


sample will she have to take? sample will she have to take?


to burn for more than 2140. [15] Estimate the number of bulbs likely

number of defective items. [15]

AWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY, HYDERABAD

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6.a) A sample of 12 fathers and their elder sons gave the following data about their

heights in inches. Calculate the coefficient of rank correlation.

Fathers 65 63 67 64 68 62 70 66 68 67 69 71

Sons 68 66 68 65 69 66 68 65 71 67 68 70

b) The equations of two Regression lines are 7x-16y+9=0, 5y-4x-3=0, find the

Coefficient of Correlation and the means of x and y. [15]

7. A fast food restaurant has one drive window. Cars arrive according to a poisson

process. Cars arrive at the rate of 2 per 5 minutes. The service time per customer

is 1.5 minutes. Determine

i) The Expected number of customers waiting to be served.

ii) The probability that the waiting line exceeds 10

iii) Average waiting time until a customer reaches the window to place an order.

iv) The probability that the facility is idle. [15]

8.a) Define Marcov Chain and give one example.

b) The school of international studies for population found out by its survey that the

mobility of the population of a state to village, town and city is in the following

percentage.

To

Village Town City

Village 30% 20% 50%

From Town 30% 50% 20%

City 10% 40% 50%

What will be the proportion of population in village, town and city after two

years? Present population has proportion of 0.4, 0.3 and 0.3 village, town and city

respectively. Find the proportions in the long run. [15]

---oo0oo---

illage 30% 20% 50%

From Town 30% 50% 20%

City 10% 40% 50%

What will be the proportion of populati

years? Present population has proportion of

respectively. Find the proportions

and give one example.

) The school of international studies for population found out by its survey that the

mobility of the population of a state to vill

To

Village Town City

illage 30% 20% 50%

From Town 30% 50% 20%

illage 30% 20% 50%

From Town 30% 50% 20%

City 10% 40% 50%




and give one example.

) The school of international studies for population found out by its survey that the

mobility of the population of a state to vill

To

Village Town City

illage 30% 20% 50%

From Town 30% 50% 20% From Town 30% 50% 20%

City 10% 40% 50%




To

Village Town City

illage 30% 20% 50%

---oo0oo---

e, town and city e, town and city 0.4, 0.3 and 0.3 villag0.4, 0.3 and 0.3 villagyears? Present population has proportion of years? Present population has proportion of years? Present population has proportion of years? Present population has proportion of years? Present population has proportion of years? Present population has proportion of years? Present population has proportion of years? Present population has proportion of years? Present population has proportion of

From Town 30% 50% 20% From Town 30% 50% 20% From Town 30% 50% 20% From Town 30% 50% 20% From Town 30% 50% 20% From Town 30% 50% 20% From Town 30% 50% 20% From Town 30% 50% 20% From Town 30% 50% 20% From Town 30% 50% 20% From Town 30% 50% 20%

Village Town City Village Town City Village Town City Village Town City Village Town City Village Town City Village Town City Village Town City Village Town City

percentage.

s for population found out by its survey that the s for population found out by its survey that the s for population found out by its survey that the s for population found out by its survey that the s for population found out by its survey that the s for population found out by its survey that the ) The school of international studie) The school of international studie) The school of international studie) The school of international studie b) The school of international studie

reaches the window to place an order. iii) Average waiting time until a customer

i) The Expected number of customers waiting to be served.

process. Cars arrive at the rate of 2 per 5 minutes. The service time per customer process. Cars arrive at the rate of 2 per 5 minutes. The service time per customer

lines are 7x-16y+9=0, 5y-4x-3=0, find the lines are 7x-16y+9=0, 5y-4x-3=0, find the b) The equations of two Regression

Sons 68 66 68 65 69 66 68 65 71 67 68 70 Sons 68 66 68 65 69 66 68 65 71 67 68 70 Sons 68 66 68 65 69 66 68 65 71 67 68 70 Sons 68 66 68 65 69 66 68 65 71 67 68 70 Sons 68 66 68 65 69 66 68 65 71 67 68 70 Sons 68 66 68 65 69 66 68 65 71 67 68 70 Sons 68 66 68 65 69 66 68 65 71 67 68 70 Sons 68 66 68 65 69 66 68 65 71 67 68 70 Sons 68 66 68 65 69 66 68 65 71 67 68 70

6.a) A sample of 12 fathers and their elde6.a) A sample of 12 fathers and their elde6.a) A sample of 12 fathers and their elder sons gave the following data about their r sons gave the following data about their r sons gave the following data about their r sons gave the following data about their 6.a) A sample of 12 fathers and their elde6.a) A sample of 12 fathers and their elde


Village Town City Village Town City

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Documents

R09 Code No: 09A30302 JAWAHARLAL NEHRU ...liet-clmc.yolasite.com/resources/Probability_and...normally distributed with an average life of 2040 hours and S.D of 40 hrs. Estimate the