3RD YEAR SEMESTER 1 SUPPLEMENTARY JUNE 2010 JNTU B.TECH ENGINEERING QUESTION PAPER- PROBABILITY AND STATISTICS

Code No:  RR311801                     RR           Set No.   2

III  B.Tech I Semester Supplementary Examinations,June 2010

PROBABILITY AND STATISTICS Metallurgy And Material Technology

Time: 3 hours                                                                                  Max Marks:  80

Answer any FIVE Questions

All  Questions carry equal marks

? ? ? ? ?

1.   (a)  2% of the  items  of a factory  are defective.   The  items  are packed  in boxes.

What  is the probability  that  there will be i. 2 defective items

ii. at least three defective items

(b)  The marks obtained in statistics in a certain examination found to be normally distributed.  If 15% of the  marks  of the  students ≥ 60, 40% < 30% marks, find the mean and standard deviation.                                                         [8+8]

2.   (a)  Fit a curve of the form y = aebx  for the following data

x	0.0	.5	1.0	1.5	2.0	2.5
y	.1	.45	2.15	9.15	40.35	180.75

(b)  Find the most possible values of x and y from the following equations  x + y

= 6, 2x - y = 2, 2x - 5y = 7, 3x - 4y = - 4                                                 [8+8]

3.   (a)  Let x be a discrete random variable having the following probability  distribu- tion, then

Find

i. K

ii. mean

iii. variance

iv.  cumulative  distribution

X	-2	-1	0	1	2	3
P(X)	0.1	k	0.2	2k	0.3	3k

(b)  The probability  that  John  hits a target  is 1 He fires 6 times.  Find the proba-

bility that  he hits the target i. exactly 2 times

ii. more than  4 times

iii. atleast  once.                                                                                              [8+8]

4. The following data  relate  to the marks of 10 students in the internal  test  and the university  examination  for the maximum  of 50 each

Internal  marks (x)	25	28	30	32	35	36	38	39	42	45
University  marks (y)	20	26	29	30	25	18	26	35	35	46

Find the coefficient of correlation  and the two lines of regression.                       [16]

1

Code No:  RR311801                     RR           Set No.   2

5.   (a)  The mean of certain  normal population  is equal to the standard error of the mean of the  samples of 64 from that  distribution.  Find  the  probability  that the mean of the sample size 36 will be negative.

(b)  A sample of 64 students have a mean weight of 70kgs. Can this be regarded as a sample from a population  with mean weight 65kgs and standard deviation

25kgs.                                                                                                               [8+8]

6.   (a)  Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing. Find the probability  that

i. both are white

ii. first is red and second is white

(b)  A businessman goes to hotels X,Y,Z 20%, 50%, 30% of the time respectively.  It is known that  5%, 4%, 8% of the rooms in X,Y,Z hotels have faulty plumbing. What  is the probability  that  business man’s room having faulty  plumbing  is assigned to hotel Z.                                                                                         [8+8]

7.   (a)  What  is the  maximum  error  can one expect  to  make  with  probability  0.90 when using the mean of a random sample of size n = 64 to estimate  the mean of a population  with σ2  = 2.56

(b)  A sample of 10 cam shafts intended  for use in gasoline engines has an average eccentricity  of 1.02 and a standard deviation of 0.044 inch. Assuming the data may be treated  a random sample from a normal population,  determine a 95% confidence interval  for the actual  mean eccentricity  of the cam shaft?

(c)  If 26 of 200 Brand A tyres fail to last 20,000 miles, whereas the corresponding figures for 200 tyres each of B,C, and D are 23, 15, and 32, use the 0.05 level of significance to test the null hypothesis that  there is no difference in the quality of four kinds of tyres with regard to their durability.                           [5+5+6]

8.   (a)  A large  electronic  firm that   hires  many  workers  with  disabilities  wants  to determine  whether  their disabilities affect such workers performance.  Use the level of significance of α = 0.05 to decide on the basis of the following data, whether it is reasonable to maintain  that  the disabilities have no effect on the worker’s performance;

Above    average               Average              Below  average

Blind	21	64	17
Deaf	16	49	14
No disability	29	93	28

(b)  It  has  been  suggested  that   an  average  college teacher  in  Andhra  Pradesh

spends  less than  10 hours  in  a  week on  his  own academic  schedule.   The figures for the time spent during a week are given below for 12 teachers:

7.1            13.1            7.8            3.6            8.4            4.9

9.6            3.4            0.1            7.2            20.3            11.1

Is the claim justified with the level of significance of 0.05?                       [8+8]

3

Code No:  RR311801                     RR           Set No.   4

III  B.Tech I Semester Supplementary Examinations,June 2010

PROBABILITY AND STATISTICS Metallurgy And Material Technology

Time: 3 hours                                                                                  Max Marks:  80

Answer any FIVE Questions

All  Questions carry equal marks

? ? ? ? ?

1.   (a)  2% of the  items  of a factory  are defective.   The  items  are packed  in boxes.

What  is the probability  that  there will be i. 2 defective items

ii. at least three defective items

(b)  The marks obtained in statistics in a certain examination found to be normally distributed.  If 15% of the  marks  of the  students ≥ 60, 40% < 30% marks, find the mean and standard deviation.                                                         [8+8]

2.   (a)  The mean of certain  normal population  is equal to the standard error of the mean of the  samples of 64 from that  distribution.  Find  the  probability  that the mean of the sample size 36 will be negative.

(b)  A sample of 64 students have a mean weight of 70kgs. Can this be regarded as

a sample from a population  with mean weight 65kgs and standard deviation

25kgs.                                                                                                               [8+8]

3. The following data  relate  to the marks of 10 students in the internal  test  and the

university  examination  for the maximum  of 50 each

Internal  marks (x)	25	28	30	32	35	36	38	39	42	45
University  marks (y)	20	26	29	30	25	18	26	35	35	46

Find the coefficient of correlation  and the two lines of regression.                       [16]

4.   (a)  What  is the  maximum  error  can one expect  to  make  with  probability  0.90 when using the mean of a random sample of size n = 64 to estimate  the mean of a population  with σ2  = 2.56

(b)  A sample of 10 cam shafts intended  for use in gasoline engines has an average eccentricity  of 1.02 and a standard deviation of 0.044 inch. Assuming the data may be treated  a random sample from a normal population,  determine a 95% confidence interval  for the actual  mean eccentricity  of the cam shaft?

(c)  If 26 of 200 Brand A tyres fail to last 20,000 miles, whereas the corresponding figures for 200 tyres each of B,C, and D are 23, 15, and 32, use the 0.05 level of significance to test the null hypothesis that  there is no difference in the quality of four kinds of tyres with regard to their durability.                           [5+5+6]

5.   (a)  A large  electronic  firm that   hires  many  workers  with  disabilities  wants  to determine  whether  their disabilities affect such workers performance.  Use the level of significance of α = 0.05 to decide on the basis of the following data, whether it is reasonable to maintain  that  the disabilities have no effect on the worker’s performance;

Above    average               Average              Below  average

Blind	21	64	17
Deaf	16	49	14
No disability	29	93	28

(b)  It  has  been  suggested  that   an  average  college teacher  in  Andhra  Pradesh spends  less than  10 hours  in  a  week on  his  own academic  schedule.   The figures for the time spent during a week are given below for 12 teachers:

7.1            13.1            7.8            3.6            8.4            4.9

9.6            3.4            0.1            7.2            20.3            11.1

Is the claim justified with the level of significance of 0.05?                       [8+8]

6.   (a)  Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing. Find the probability  that

i. both are white

ii. first is red and second is white

(b)  A businessman goes to hotels X,Y,Z 20%, 50%, 30% of the time respectively.  It is known that  5%, 4%, 8% of the rooms in X,Y,Z hotels have faulty plumbing. What  is the probability  that  business man’s room having faulty  plumbing  is assigned to hotel Z.                                                                                         [8+8]

7.   (a)  Fit a curve of the form y = aebx  for the following data

x	0.0	.5	1.0	1.5	2.0	2.5
y	.1	.45	2.15	9.15	40.35	180.75

(b)  Find the most possible values of x and y from the following equations  x + y

= 6, 2x - y = 2, 2x - 5y = 7, 3x - 4y = - 4                                                 [8+8]

8.   (a)  Let x be a discrete random variable having the following probability  distribu- tion, then

Find

i. K

ii. mean

iii. variance

iv.  cumulative  distribution

5

Code No:  RR311801                     RR           Set No.   4

X	-2	-1	0	1	2	3
P(X)	0.1	k	0.2	2k	0.3	3k

(b)  The probability  that  John  hits a target  is 1 He fires 6 times.  Find the proba-

bility that  he hits the target i. exactly 2 times

ii. more than  4 times

iii. atleast  once.                                                                                              [8+8]

Code No:  RR311801                     RR           Set No.   1

III  B.Tech I Semester Supplementary Examinations,June 2010

PROBABILITY AND STATISTICS Metallurgy And Material Technology

Time: 3 hours                                                                                  Max Marks:  80

Answer any FIVE Questions

All  Questions carry equal marks

? ? ? ? ?

1.   (a)  The mean of certain  normal population  is equal to the standard error of the mean of the  samples of 64 from that  distribution.  Find  the  probability  that the mean of the sample size 36 will be negative.

(b)  A sample of 64 students have a mean weight of 70kgs. Can this be regarded as a sample from a population  with mean weight 65kgs and standard deviation

25kgs.                                                                                                               [8+8]

2.   (a)  Fit a curve of the form y = aebx  for the following data

x	0.0	.5	1.0	1.5	2.0	2.5
y	.1	.45	2.15	9.15	40.35	180.75

(b)  Find the most possible values of x and y from the following equations  x + y

= 6, 2x - y = 2, 2x - 5y = 7, 3x - 4y = - 4                                                 [8+8]

3.   (a)  2% of the  items  of a factory  are defective.   The  items  are packed  in boxes.

What  is the probability  that  there will be i. 2 defective items

ii. at least three defective items

(b)  The marks obtained in statistics in a certain examination found to be normally distributed.  If 15% of the  marks  of the  students ≥ 60, 40% < 30% marks, find the mean and standard deviation.                                                         [8+8]

4.   (a)  A large  electronic  firm that   hires  many  workers  with  disabilities  wants  to determine  whether  their disabilities affect such workers performance.  Use the level of significance of α = 0.05 to decide on the basis of the following data, whether it is reasonable to maintain  that  the disabilities have no effect on the worker’s performance;

Above    average               Average              Below  average

Blind	21	64	17
Deaf	16	49	14
No disability	29	93	28

(b)  It  has  been  suggested  that   an  average  college teacher  in  Andhra  Pradesh spends  less than  10 hours  in  a  week on  his  own academic  schedule.   The figures for the time spent during a week are given below for 12 teachers:

7

Code No:  RR311801                     RR           Set No.   1

7.1            13.1            7.8            3.6            8.4            4.9

9.6            3.4            0.1            7.2            20.3            11.1

Is the claim justified with the level of significance of 0.05?                       [8+8]

5.   (a)  Let x be a discrete random variable having the following probability  distribu- tion, then

Find

i. K

ii. mean

iii. variance

iv.  cumulative  distribution

X	-2	-1	0	1	2	3
P(X)	0.1	k	0.2	2k	0.3	3k

(b)  The probability  that  John  hits a target  is 1 He fires 6 times.  Find the proba-

bility that  he hits the target i. exactly 2 times

ii. more than  4 times

iii. atleast  once.                                                                                              [8+8]

6.   (a)  What  is the  maximum  error  can one expect  to  make  with  probability  0.90 when using the mean of a random sample of size n = 64 to estimate  the mean of a population  with σ2  = 2.56

(b)  A sample of 10 cam shafts intended  for use in gasoline engines has an average eccentricity  of 1.02 and a standard deviation of 0.044 inch. Assuming the data may be treated  a random sample from a normal population,  determine a 95% confidence interval  for the actual  mean eccentricity  of the cam shaft?

(c)  If 26 of 200 Brand A tyres fail to last 20,000 miles, whereas the corresponding figures for 200 tyres each of B,C, and D are 23, 15, and 32, use the 0.05 level of significance to test the null hypothesis that  there is no difference in the quality of four kinds of tyres with regard to their durability.                           [5+5+6]

7. The following data  relate  to the marks of 10 students in the internal  test  and the university  examination  for the maximum  of 50 each

Internal  marks (x)	25	28	30	32	35	36	38	39	42	45
University  marks (y)	20	26	29	30	25	18	26	35	35	46

Find the coefficient of correlation  and the two lines of regression.                       [16]

8.   (a)  Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing. Find the probability  that

8

Code No:  RR311801                     RR           Set No.   1

i. both are white

ii. first is red and second is white

(b)  A businessman goes to hotels X,Y,Z 20%, 50%, 30% of the time respectively.  It is known that  5%, 4%, 8% of the rooms in X,Y,Z hotels have faulty plumbing. What  is the probability  that  business man’s room having faulty  plumbing  is assigned to hotel Z.                                                                                         [8+8]

Code No:  RR311801                     RR           Set No.   3

III  B.Tech I Semester Supplementary Examinations,June 2010

PROBABILITY AND STATISTICS Metallurgy And Material Technology

Time: 3 hours                                                                                  Max Marks:  80

Answer any FIVE Questions

All  Questions carry equal marks

? ? ? ? ?

1. The following data  relate  to the marks of 10 students in the internal  test  and the university  examination  for the maximum  of 50 each

Internal  marks (x)	25	28	30	32	35	36	38	39	42	45
University  marks (y)	20	26	29	30	25	18	26	35	35	46

Find the coefficient of correlation  and the two lines of regression.                       [16]

2.   (a)  2% of the  items  of a factory  are defective.   The  items  are packed  in boxes.

What  is the probability  that  there will be i. 2 defective items

ii. at least three defective items

(b)  The marks obtained in statistics in a certain examination found to be normally distributed.  If 15% of the  marks  of the  students ≥ 60, 40% < 30% marks, find the mean and standard deviation.                                                         [8+8]

3.   (a)  Let x be a discrete random variable having the following probability  distribu- tion, then

Find

i. K

ii. mean

iii. variance

iv.  cumulative  distribution

X	-2	-1	0	1	2	3
P(X)	0.1	k	0.2	2k	0.3	3k

(b)  The probability  that  John  hits a target  is 1 He fires 6 times.  Find the proba-

bility that  he hits the target i. exactly 2 times

ii. more than  4 times

iii. atleast  once.                                                                                              [8+8]

4.   (a)  Fit a curve of the form y = aebx  for the following data

x	0.0	.5	1.0	1.5	2.0	2.5
y	.1	.45	2.15	9.15	40.35	180.75

10

Code No:  RR311801                     RR           Set No.   3

(b)  Find the most possible values of x and y from the following equations  x + y

= 6, 2x - y = 2, 2x - 5y = 7, 3x - 4y = - 4                                                 [8+8]

5.   (a)  The mean of certain  normal population  is equal to the standard error of the mean of the  samples of 64 from that  distribution.  Find  the  probability  that the mean of the sample size 36 will be negative.

(b)  A sample of 64 students have a mean weight of 70kgs. Can this be regarded as a sample from a population  with mean weight 65kgs and standard deviation

25kgs.                                                                                                               [8+8]

6.   (a)  What  is the  maximum  error  can one expect  to  make  with  probability  0.90 when using the mean of a random sample of size n = 64 to estimate  the mean of a population  with σ2  = 2.56

(b)  A sample of 10 cam shafts intended  for use in gasoline engines has an average eccentricity  of 1.02 and a standard deviation of 0.044 inch. Assuming the data may be treated  a random sample from a normal population,  determine a 95% confidence interval  for the actual  mean eccentricity  of the cam shaft?

(c)  If 26 of 200 Brand A tyres fail to last 20,000 miles, whereas the corresponding figures for 200 tyres each of B,C, and D are 23, 15, and 32, use the 0.05 level of significance to test the null hypothesis that  there is no difference in the quality of four kinds of tyres with regard to their durability.                           [5+5+6]

7.   (a)  A large  electronic  firm that   hires  many  workers  with  disabilities  wants  to determine  whether  their disabilities affect such workers performance.  Use the level of significance of α = 0.05 to decide on the basis of the following data, whether it is reasonable to maintain  that  the disabilities have no effect on the worker’s performance;

Above    average               Average              Below  average

Blind	21	64	17
Deaf	16	49	14
No disability	29	93	28

(b)  It  has  been  suggested  that   an  average  college teacher  in  Andhra  Pradesh spends  less than  10 hours  in  a  week on  his  own academic  schedule.   The figures for the time spent during a week are given below for 12 teachers:

7.1            13.1            7.8            3.6            8.4            4.9

9.6            3.4            0.1            7.2            20.3            11.1

Is the claim justified with the level of significance of 0.05?                       [8+8]

8.   (a)  Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing. Find the probability  that

11

Code No:  RR311801                     RR           Set No.   3

i. both are white

ii. first is red and second is white

(b)  A businessman goes to hotels X,Y,Z 20%, 50%, 30% of the time respectively.  It is known that  5%, 4%, 8% of the rooms in X,Y,Z hotels have faulty plumbing. What  is the probability  that  business man’s room having faulty  plumbing  is assigned to hotel Z.                                                                                         [8+8]