R09 - December, 2011 - Regular Examinations - Set - 4.

II B.Tech I Semester Examinations,December 2011
PROBABILITY AND STATISTICS
Common to ME, MECT, MEP, AME, CSE
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
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1. (a) The mean height of students in a college is 155 cms and standard deviation is
15. What is the probability that the mean height of 36 students is less than
157 cms.
(b) Given that the mean height of students in a class is 158 cms with a standard
deviation of 20 cms. Find how many students heights lie
i. Between 150 cms and 170 cms.
ii. Above 180 cms. [7 8]
2. A gambler has Rs.2. He bets Rs.1 at a time and wins Rs.1 with probability 0.5.
He stops Playing if he looses Rs.2 or wins Rs.4.
(a) What is the Transition probability matrix of the related markov chain?
(b) What is the probability that he has lost his money at the end of 5 plays? [15]
3. (a) The number of automobile accidents per week in a certain community are as
follows : 12, 8, 20, 2, 14, 10, 15, 6, 9, 4 are these frequencies in agreement with
the belief that accident conditions were two same during this 10 week period.
(b) A die is thrown 264 times with the following results. Show that the die is
biased.(Given X2
0:05 =11.07 for 5 d.f) [15]
No. appeared on the die  1     2    3    4    5    6
Frequency                    40   32   28  58   54  52
4. (a) A manufacturer claimed that at least 95% of the equipment which he supplied
to a factory conformed to speci cations. An examination of a sample of 200
pieces of equipments received 80 were faulty. Test the claim at .05 level.
(b) A machine puts out 9 imperfect articles in a sample of 200 articles. After
the Machine is overhauled it puts out 5 imperfect articles in a sample of 700
articles. Test at 5% level whether the Machine is improved? [15]
5. (a) Given n=10, x = 5.4, y = 6.2 and sum of the product of deviation from
the mean of X and Y is 66 nd the correlation co-e cient.
(b) If the two regression lines of y on x and x on y are respectives a1x b1y c1 = 0
and a2x b2y c2 = 0 prove that a1 b2 < 2b1 [15]
6. (a) A random sample of 500 points on a heated plate resulted in an average
temperature of 73.54 degrees Fahrenheit with a standard deviation of 2.79
degree Fahrenheit. Find a 99% con dence interval for the average temperature
of the plate.

(b) An aircraft strobe light is designed so that the times between 
ashes have a
mean of 10.15 s and a standard deviation of 0.4 s. O cials at the airport
want to check if the strobe light needs adjustment. A sample of 50 times is
randomly selected and the mean time between 
ashes is 9.87 Use the 5% level
of signi cance. [7 8]
7. Consider a box o ce ticket window being manned by a single server. Customer
arrive to purchase tickets according to poisson input process with a mean rate of
30 per hour. The time required to serve a customer has an exponential distribution
with a mean of 910 seconds. Determine the following.
(a) Fraction of the time the server is busy.
(b) The average number of customers queuing for service. [15]
8. (a) If A,B and C are three events prove that
P (A [ B [ C) = P (A) P (B) P (C) ?? P (A \ B)
??P (B \ C) P (C \ A) P (A \ B \ C)
(b) For the discrete probility distribution
x 0 1 2 3 4 5 6 7
f 0 k 2k 2k 3K k2 2k2 7k2 k
Determine:
(a) K
(b) mean
(c) variance. [8 7]
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