NR
Code No: NR220105
Set No. 2
in
II B.Tech II Semester Supplimentry Examinations,May 2010 PROBABILITY AND STATISTICS Common to CE, CHEM, IT, MEP, E.COMP.E, CSE, CSSE Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) If A is independent of B, B∪C and B∩C, show that it is also independent of C.
ld .
(b) In a group of employed persons, 28% are women 60% of the men and 40% of the women pay income tax . Find the probability that a randomly selected person does not pay income tax. [8+8] 2. (a) Find the mean and standard deviation of a normal distribution in which 7% of the items one under 35 and 89% are under 63.
3. Use r =
to find r for the following data.
21 23 30 54 57 58 60 71 72 83 110 84
[16]
72 78 87 90 100 92 113 135
uW
x: y:
2 σx2 + σy2 + σx−y 2σx σy
or
(b) The number of e-mails received by a computer is at the rate of two per 3 minutes. Determine the probability that five or more e-mails are received in duration of a 9 minutes. [8+8]
4. (a) Predict y at x=5 by fitting a least squares straight line to the following data:
2
y
1.8
4
6
8
10
12
1.5
1.4
1.1
1.1
0.9
nt
x
Aj
(b) Construct a 95% confidence interval for α (c) Test null hypotheris β = - 0.12 against β > - 0.12 at 0.01 level of significance. [6+4+6]
5. (a) The voltage of a battery is very nearly normal with mean 15.0 volts and standard deviation 0.2 volts. What is the probability that four such batteries connected in series will have a combined voltage of 60.8 or more volts? (b) For a chi-squared distribution find Xα2 such that i. P(X2 > Xα2 ) = 0.99 when υ = 4 ii. P (37.652 < X2
[8+8]
Code No: NR220105
NR
Set No. 2
6. (a) A coin is tossed 960 times and it falls with head upwards 184 times. Is the coin biased? (b) A die is thrown 9000 times and a throw of 3 or 4 observed 3240 times. Show that the die cannot be regarded as an unbiased one. [8+8]
in
7. (a) A random sample of 6 steel beams has a mean compressive strength of 58,392 psi (pounds per square inch) with a standard deviation of 648 psi. Use this information and level of significance α = 0.05 to test whether the true average compressive strength of the steel from which this sample came is 58,000 psi.
ld .
(b) Measurements of the fat content of two kinds of ice cream, Brand A and Brand B, yielded the following sample data: Test the null hypothesis µ1 = µ2 (where 13.5 14 13.6 12.9 Brand A (%)
13
12.9 13 12.4 13.5 12.7
or
Brand B (%)
uW
µ1 and µ2 are the respective true average fat contents of the two kinds of ice cream) against the alternative hypothesis µ16= µ2 at the level of significance α =0.05. Test the null hypothesis µ1 = µ2 (where µ1 and µ2 are the respective true average fat contents of the two kinds of ice cream) against the alternative hypothesis µ16= µ2 at the level of significance α =0.05. [8+8] 8. (a) Find the probability, and that number of driving licenses X issued by Road Transport Authority (RTA) in a specific month is between 64 and 184 if the number of driving licenses issued X is a random variable with µ = 124 and σ=7.5., using chebyshev’s theorem
Aj
nt
(b) The daily consumption of electric power (in millions of kw hours) is a random n −x/3 1 ,x >0 f (x) = 9 xe If the total production is variable having the PDF 0 , x≤0 12 million kw hours, determine the probability that there is power-cut (shortage) on any given day. [8+8] ?????
2
NR
Code No: NR220105
Set No. 4
x: y:
2 σx2 + σy2 + σx−y 2σx σy
to find r for the following data.
21 23 30 54 57 58 60 71 72 83 110 84
[16]
72 78 87 90 100 92 113 135
ld .
1. Use r =
in
II B.Tech II Semester Supplimentry Examinations,May 2010 PROBABILITY AND STATISTICS Common to CE, CHEM, IT, MEP, E.COMP.E, CSE, CSSE Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????
2. (a) Find the probability, and that number of driving licenses X issued by Road Transport Authority (RTA) in a specific month is between 64 and 184 if the number of driving licenses issued X is a random variable with µ = 124 and σ=7.5., using chebyshev’s theorem
uW
or
(b) The daily consumption of electric power (in millions of kw hours) is a random n x − f (x) = 19 xe /3 , x > 0 variable having the PDF If the total production is 0 , x≤0 12 million kw hours, determine the probability that there is power-cut (shortage) on any given day. [8+8] 3. (a) A random sample of 6 steel beams has a mean compressive strength of 58,392 psi (pounds per square inch) with a standard deviation of 648 psi. Use this information and level of significance α = 0.05 to test whether the true average compressive strength of the steel from which this sample came is 58,000 psi. (b) Measurements of the fat content of two kinds of ice cream, Brand A and Brand B, yielded the following sample data: Test the null hypothesis µ1 = µ2 (where 13.5 14 13.6 12.9
13
nt
Brand A (%)
12.9 13 12.4 13.5 12.7
Aj
Brand B (%)
µ1 and µ2 are the respective true average fat contents of the two kinds of ice cream) against the alternative hypothesis µ16= µ2 at the level of significance α =0.05. Test the null hypothesis µ1 = µ2 (where µ1 and µ2 are the respective true average fat contents of the two kinds of ice cream) against the alternative hypothesis µ16= µ2 at the level of significance α =0.05. [8+8]
4. (a) If A is independent of B, B∪C and B∩C, show that it is also independent of C. 3
NR
Code No: NR220105
Set No. 4
(b) In a group of employed persons, 28% are women 60% of the men and 40% of the women pay income tax . Find the probability that a randomly selected person does not pay income tax. [8+8] 5. (a) Find the mean and standard deviation of a normal distribution in which 7% of the items one under 35 and 89% are under 63.
in
(b) The number of e-mails received by a computer is at the rate of two per 3 minutes. Determine the probability that five or more e-mails are received in duration of a 9 minutes. [8+8]
2
4
6
8
y
1.8
1.5
1.4
1.1
10
12
1.1
0.9
or
x
ld .
6. (a) Predict y at x=5 by fitting a least squares straight line to the following data:
(b) Construct a 95% confidence interval for α
uW
(c) Test null hypotheris β = - 0.12 against β > - 0.12 at 0.01 level of significance. [6+4+6] 7. (a) The voltage of a battery is very nearly normal with mean 15.0 volts and standard deviation 0.2 volts. What is the probability that four such batteries connected in series will have a combined voltage of 60.8 or more volts? (b) For a chi-squared distribution find Xα2 such that
nt
i. P(X2 > Xα2 ) = 0.99 when υ = 4 ii. P (37.652 < X2
[8+8]
8. (a) A coin is tossed 960 times and it falls with head upwards 184 times. Is the coin biased?
Aj
(b) A die is thrown 9000 times and a throw of 3 or 4 observed 3240 times. Show that the die cannot be regarded as an unbiased one. [8+8] ?????
4
NR
Code No: NR220105
Set No. 1
in
II B.Tech II Semester Supplimentry Examinations,May 2010 PROBABILITY AND STATISTICS Common to CE, CHEM, IT, MEP, E.COMP.E, CSE, CSSE Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Predict y at x=5 by fitting a least squares straight line to the following data:
4
6
8
y
1.8
1.5
1.4
1.1
10
12
ld .
2
1.1
0.9
or
x
(b) Construct a 95% confidence interval for α
(c) Test null hypotheris β = - 0.12 against β > - 0.12 at 0.01 level of significance. [6+4+6]
uW
2. (a) Find the probability, and that number of driving licenses X issued by Road Transport Authority (RTA) in a specific month is between 64 and 184 if the number of driving licenses issued X is a random variable with µ = 124 and σ=7.5., using chebyshev’s theorem
nt
(b) The daily consumption of electric power (in millions of kw hours) is a random n −x/3 1 ,x >0 f (x) = 9 xe If the total production is variable having the PDF 0 , x≤0 12 million kw hours, determine the probability that there is power-cut (shortage) on any given day. [8+8]
3. (a) If A is independent of B, B∪C and B∩C, show that it is also independent of C.
Aj
(b) In a group of employed persons, 28% are women 60% of the men and 40% of the women pay income tax . Find the probability that a randomly selected person does not pay income tax. [8+8]
4. (a) A random sample of 6 steel beams has a mean compressive strength of 58,392 psi (pounds per square inch) with a standard deviation of 648 psi. Use this information and level of significance α = 0.05 to test whether the true average compressive strength of the steel from which this sample came is 58,000 psi. (b) Measurements of the fat content of two kinds of ice cream, Brand A and Brand B, yielded the following sample data: Test the null hypothesis µ1 = µ2 (where µ1 and µ2 are the respective true average fat contents of the two kinds of ice 5
NR
Code No: NR220105
Set No. 1
13.5 14 13.6 12.9
13
Brand A (%) 12.9 13 12.4 13.5 12.7
in
Brand B (%)
ld .
cream) against the alternative hypothesis µ16= µ2 at the level of significance α =0.05. Test the null hypothesis µ1 = µ2 (where µ1 and µ2 are the respective true average fat contents of the two kinds of ice cream) against the alternative hypothesis µ16= µ2 at the level of significance α =0.05. [8+8]
5. (a) A coin is tossed 960 times and it falls with head upwards 184 times. Is the coin biased?
6. Use r =
to find r for the following data.
21 23 30 54 57 58 60 71 72 83 110 84
[16]
72 78 87 90 100 92 113 135
uW
x: y:
2 σx2 + σy2 + σx−y 2σx σy
or
(b) A die is thrown 9000 times and a throw of 3 or 4 observed 3240 times. Show that the die cannot be regarded as an unbiased one. [8+8]
7. (a) The voltage of a battery is very nearly normal with mean 15.0 volts and standard deviation 0.2 volts. What is the probability that four such batteries connected in series will have a combined voltage of 60.8 or more volts? (b) For a chi-squared distribution find Xα2 such that i. P(X2 > Xα2 ) = 0.99 when υ = 4 ii. P (37.652 < X2
[8+8]
nt
8. (a) Find the mean and standard deviation of a normal distribution in which 7% of the items one under 35 and 89% are under 63.
Aj
(b) The number of e-mails received by a computer is at the rate of two per 3 minutes. Determine the probability that five or more e-mails are received in duration of a 9 minutes. [8+8] ?????
6
NR
Code No: NR220105
Set No. 3
in
II B.Tech II Semester Supplimentry Examinations,May 2010 PROBABILITY AND STATISTICS Common to CE, CHEM, IT, MEP, E.COMP.E, CSE, CSSE Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) A coin is tossed 960 times and it falls with head upwards 184 times. Is the coin biased?
ld .
(b) A die is thrown 9000 times and a throw of 3 or 4 observed 3240 times. Show that the die cannot be regarded as an unbiased one. [8+8] 2. (a) Predict y at x=5 by fitting a least squares straight line to the following data:
4
6
y
1.8
1.5
1.4
8
10
or
2
1.1
1.1
12
0.9
uW
x
(b) Construct a 95% confidence interval for α (c) Test null hypotheris β = - 0.12 against β > - 0.12 at 0.01 level of significance. [6+4+6] 3. (a) If A is independent of B, B∪C and B∩C, show that it is also independent of C.
nt
(b) In a group of employed persons, 28% are women 60% of the men and 40% of the women pay income tax . Find the probability that a randomly selected person does not pay income tax. [8+8]
Aj
4. (a) Find the probability, and that number of driving licenses X issued by Road Transport Authority (RTA) in a specific month is between 64 and 184 if the number of driving licenses issued X is a random variable with µ = 124 and σ=7.5., using chebyshev’s theorem (b) The daily consumption of electric power (in millions of kw hours) is a random n x f (x) = 19 xe− /3 , x > 0 If the total production is variable having the PDF 0 , x≤0 12 million kw hours, determine the probability that there is power-cut (shortage) on any given day. [8+8]
5. (a) A random sample of 6 steel beams has a mean compressive strength of 58,392 psi (pounds per square inch) with a standard deviation of 648 psi. Use this 7
NR
Code No: NR220105
Set No. 3
information and level of significance α = 0.05 to test whether the true average compressive strength of the steel from which this sample came is 58,000 psi. (b) Measurements of the fat content of two kinds of ice cream, Brand A and Brand B, yielded the following sample data: Test the null hypothesis µ1 = µ2 (where 13
Brand A (%) 12.9 13 12.4 13.5 12.7
ld .
Brand B (%)
in
13.5 14 13.6 12.9
6. Use r =
to find r for the following data.
21 23 30 54 57 58 60 71 72 83 110 84
[16]
72 78 87 90 100 92 113 135
uW
x: y:
2 σx2 + σy2 + σx−y 2σx σy
or
µ1 and µ2 are the respective true average fat contents of the two kinds of ice cream) against the alternative hypothesis µ16= µ2 at the level of significance α =0.05. Test the null hypothesis µ1 = µ2 (where µ1 and µ2 are the respective true average fat contents of the two kinds of ice cream) against the alternative hypothesis µ16= µ2 at the level of significance α =0.05. [8+8]
7. (a) The voltage of a battery is very nearly normal with mean 15.0 volts and standard deviation 0.2 volts. What is the probability that four such batteries connected in series will have a combined voltage of 60.8 or more volts? (b) For a chi-squared distribution find Xα2 such that
nt
i. P(X2 > Xα2 ) = 0.99 when υ = 4 ii. P (37.652 < X2
[8+8]
8. (a) Find the mean and standard deviation of a normal distribution in which 7% of the items one under 35 and 89% are under 63.
Aj
(b) The number of e-mails received by a computer is at the rate of two per 3 minutes. Determine the probability that five or more e-mails are received in duration of a 9 minutes. [8+8] ?????
8
