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Posted By: kondapalli Member Level: Gold Posted Date: 07 May 2008
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2007 Jawaharlal Nehru Technological University B.Tech Computer Science & Engineering PROBABILITY AND STATISTICS setno2 Question paper
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1. (a) The probabilities that students A,B,C,D solve a problem are 1/3, 2/5, 1/5
and 1/4 respectively. If all of them try to solve the problem, what is the
probability that the problem is solved.
(b) In a bolt factory machines A,B,C manufacture 20%, 30% and 50% of the total
of their output and 6%, 3% and 2% are defective. A bolt is drawn at random
and found to be defective. Find the probabilities that it is manufactured from
i. Machine A
ii. Machine B
iii. Machine C [8+8]
2. (a) For the continuous probability functionf(x) = kx2e-x when x 0, find
i. k
ii. mean
iii. variance
(b) 20% of items produced from a factory are defective. Find the probability that
in a sample of 5 chosen at random.
i. none is defective
ii. one is defective
iii. p(1 < x < 4) [8+8]
3. (a) Average number of accidents on any day on a national highway is 1.8. Deter-
mine the probability that the number of accidents are
i. at least one
ii. at most one
(b) If X is a normal variate, Find the probability
i. to the left of z = -1.78
ii. to the right of z = - 1.45
iii. corresponding to - 0.80 z 1.53
iv. to the left of z= - 2.52 and to the right of z= 1.83. [8+8]
4. Take 30 slips of paper and label 5 each -4 and 4, four each - 3 and 3, three each -
2 and 2 and each-1, 0 and 1, if each slip of the paper has the same probability of
being drown find the probabilities of getting - 4,- 3, - 2, - 1, 0, 1, 2, 3, 4 and find
the mean and varience of this distribution of means. [16]
5. (a) In a random sample of 400 industrial accidents, it was found that 231 were
due atleast partially to unsafe working conditions. Construct a 99% percent
confidence interval for the corresponding true proportion?
(b) In a study designed to investigate whether certain detonators used with ex-
plosives in coal mining meet the requirement that at least 90% will ignite
the explosive when charged, it is found that 174 of 200 detonators function
properly. Find a 95% confidence interval for the true proportion? [8+8]
6. The following is the distribution of hourly number of trucks arriving at a company’s
warehouse;
No.of Trucks 0 1 2 3 4 5 6 7 8
Frequency 52 151 130 102 45 12 5 1 2
Find the mean of this distribution, and using it as parameter ?, fit a Poisson
distribution. Test for goodness of fit at the 0.05 level of significance? [16]
7. (a) The following data pertain to the number of computer jobs per day and the
required CPU time required:
Number of jobs X 1 2 3 4 5
CPU time Y 2 5 4 9 10
Fit a least square line to estimate the mean CPU time and using it estimate
the CPU time at x = 3.5.
(b) Fit a parabola of the from y = ao + a1x + a2x2 to the following data: by the
method of least squares and estimate y at x=7.5.
x 1 2 3 4 5 6 7 8 9 10
y 1.28 1.53 1.03 0.81 0.74 0.65 0.87 0.81 1.10 1.03
The method of least squares and estimate Y at X = 7.5 [8+8]
8. (a) The regression equations of two variables x and y are
x = 0.7 y + 5.2, y = 0.3x + 2.8. Find the means of the variables and the
coefficient of correlation between them
(b) Consider the following data:
x -4 -3 -2 -1 0 1 2 3 4
y 0.1 2.5 3.4 3.9 4.1 3.8 3.5 2.8 0.3
Find the correlation coefficient ‘r’. [6+10]
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