RR220105 Probability & Statistics B.Tech Question Paper : djriet.edu.in
Name of the College : Dasari Jhansi Rani Institute Of Engineering And Technology
University : JNTUK
Department : Computer Science And Engineering
Subject Code/Name : RR220105 – Probability And Statistics
Year : 2008
Degree :B.Tech
Year/Sem : II/II
Website : djriet.edu.in
Document Type : Model Question Paper
Probability And Statistics : https://www.pdfquestion.in/uploads/djriet.edu.in/2969-RR220105-PROBABILITY-AND-STATISTICS.pdf
DJRIET Probability & Statistics Question Paper
II B.Tech II Semester Supplimentary Examinations, Apr/May 2008 :
PROBABILITY AND STATISTICS :
( Common to Civil Engineering, Mechanical Engineering, Computer Science & Engineering, Chemical Engineering, Information Technology, Mechatronics, Computer Science & Systems Engineering, Electronics & Computer Engineering, Production Engineering, Bio-Technology and Automobile Engineering)
Time: 3 hours
Max Marks: 80
Answer any FIVE Questions :
Related : Dasari Jhansi Rani Institute Of Engineering And Technology RR320403 Electronic Measurements And Instrumentation B.Tech Question Paper : www.pdfquestion.in/3023.html
Set – I
All Questions carry equal marks :
1. (a) The probabilities of passing in subject A, B, C, D are 3/4, 2/3, 4/5 and 1/2 respectively. To qualify in the examination a student should pass in A and two subjects among the three what is the probability of qualifying in that examination.
(b) There are two boxes. In box -I, 11 cards are there numbered 1 to 11 and in box-II, 5 cards numbered 1 to 5. A box is chosen and a card is drawn. If the card shows an even number then another card is drawn from the same box. If card shows an odd number another card is drawn from the other box. Find the probability that
i. Both are even
ii. Both are odd
iii. If both are even, it is from box I. [8+8]
2. (a) For the continuous probability function f (x) = kx2 e-x 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) Find the probability that at most 5 defective components will be found in a lot of 200 it experience. Shows that 2% of such components are defective. Also find the probability of more than five defective components.
(b) Write the importance of normal distribution.
(c) If the mean and S.D of normal distribution are 70 and 16, find
p(x=38) < x <p(x=45)
[8+8]
1 of 2
4. To compare two kinds of bumper guards, 6 od each kind were monted on a car and then the car has ran into a concrete wall. The following are the costs of repairs:
Guard1 107 148 123 165 102 119
Guard2 134 115 112 151 133 129
Use the 0.01 level of significance to test whether the difference between two sample means is significant? [16]
5. (a) A sample of size 64 and mean 60 was taken from a population whose standard deviation is 10. Find 95% confidence interval for the mean.
(b) Experience has shown that 10% of a manufactured product is of top quality. What can you say about the maximum error with 95% confidence for 100 items
(c) A coin is tossed 512 times. Head turned up 244 times. Can you say that the coin is unbiased. [5+5+6]
6. (a) A random sample from a company’s very extensive files shows that the orders for a certain kind of machinery were filed, respectively in 10,12,19,14,15,18,11 and 13 days. Use the level of significance a=0.01 to test the claim that on the average such orders are field in 10.5 days. Assume normality?
(b) The results of polls conducted 2 weeks and 4 weeks before a gubernatorial election are shown in the following table:
Two weeks before election Four weeks before election
For Republican canditate 79 91
For Democratic canditate 84 66
Undecided 37 43
Use the 0.05 level of significance to test whether there has been a change in opinion during the 2 weeks between the polls. [8+8]
7. (a) Derive normal equations to fit a parabola y = a0 + a1x + a2x2
(b) Fit the curve y = aebx for the following data [6+10]
x 1 5 7 9 12
y 10 15 12 15 21
Set – II
1. (a) For any three arbitrary events A, B, C , 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) In a certain town 40% have brown hair, 25% have brown eyes and 15% have both brown hair and brown eyes. A person is select at random from the town
i. If he has brown hair, what is the probability that he has brown eyes also
ii. If he has brown eyes, determine the probability that he does not have brown hair [8+8]
2. (a) Define random variable, discrete probability distribution, continuous probability distribution and cumulative distribution. Give an example of each.
(b) Assume that 50% of all engineering students are good in mathematics. Determine the probabilities that among 18 engineering students
i. exactly 10
ii. at least 10
iii. at most 8
iv. at least 2 and at most 9 , are good in mathematics. [8+8]
3. (a) Show that the mean and variance of a Poisson distribution are equal.
(b) Determine the minimum mark a student should get in order to receive an A grade if the top 10% of the students are awarded A grades in an examination where the mean mark is 72 and standard deviation is 9. [8+8]
4. (a) The mean life time of light bulbs produced by company is 1500 hours with standard deviation of 150 hours. Determine the probability that lighting will take place for
i. at least 5000 hours
ii. at most 4200 hours if three bulbs are connected such that when one bulb burns out another bulb will go on. Assume that the life times are normally distributed.
(b) Find the probability that random samples of 100 bolts, chosen from a lot of 500 bolts having mean weight of 142.30 gms and standard deviation of 8.50 gms, will have a combined weight of
i. between 14061 and 14175 gms
ii. more than 14460 gms. [8+8]
5. (a) A random sample of size 100 has a standard deviation of 5. What can you say about the maximum error with 95% confidence.
(b) Among 900 people in a state 90 are found to be chapatti eaters. Construct 99% confidence interval for the true proportion.
(c) A random sample of 1200 apples was taken from a large consignment and found that 10% of them are bad. The supplier claims that only 2% are bad. Test his claim at 95% level. [5+5+6]