Download JNTU Anantapur (JNTU Anantapur) Master of Computer Applications (MCA) 2019 May Reg-Supply 1st Sem 17FBS101 Probability And Statistics Previous Question Paper
MCA I Semester Supplementary Examinations May/June 2019
PROBABILITY & STATISTICS
(For students admitted in 2017 & 2018 only)
Time: 3 hours Max. Marks: 60
Answer all the questions
*****
1 (a) The mean and variance of a binomial distribution are 4 and 4/3 respectively. Find ?? ( ?? ?1).
(b) If the variance of a Poisson variate is 3, then find the probability that:
(i) ?? =0. (ii) 0 < ?? ?3. (ii) 1 ? ?? <4.
OR
2 (a) Find the probability of getting a sum of 10 if we throw two dice.
(b) A bag A contains 2 white and 3 red balls and a bag B contains 4 white and 5 red balls. One
ball is drawn at random from one of the bags and it is found to be red. Find the probability that
the red ball drawn is from bag B.
3 In a random sample of 60 workers, the average time taken by them to get to work is 33.8
minutes with a standard deviation of 6.1 minutes. Can we reject the null hypothesis ?? =32.6
minutes in favor of alternative null hypothesis ?? >32.6 and ?? =0.025 level of significance.
OR
4 A random sample of size 25 from a normal population has the mean ?? =47.5 and standard
deviation ?? =8.4. Does the information tend to support or refute the claim the mean of
population is ?? =42.5?
5 A tea company appoints four salesmen A, B, C and D and observe their sales in three
seasons- summer, winter and monsoon. The figures (in lakhs) are given in the below table.
Seasons
Sales men
Seasons total
A B C D
Summer 36 36 21 35 128
Winter 28 29 31 32 120
Monsoon 26 28 29 29 112
Sales totals 90 93 81 96 360
(i) DO the salesmen significantly differ in performance?
(ii) Is there significant difference between the seasons?
OR
6 To assess the significance of possible variation in performance in a certain test between the
convent schools of a city, a common test was given to a number of students taken at random
from fifth class of each of the four schools concerned. The results are given below. Make
analysis of variance of data.
Schools
A B C D
8 12 18 13
10 11 12 9
12 9 16 12
8 14 6 16
7 4 8 15
Contd. in page 2
Page 1 of 2
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Code: 17FBS101
MCA I Semester Supplementary Examinations May/June 2019
PROBABILITY & STATISTICS
(For students admitted in 2017 & 2018 only)
Time: 3 hours Max. Marks: 60
Answer all the questions
*****
1 (a) The mean and variance of a binomial distribution are 4 and 4/3 respectively. Find ?? ( ?? ?1).
(b) If the variance of a Poisson variate is 3, then find the probability that:
(i) ?? =0. (ii) 0 < ?? ?3. (ii) 1 ? ?? <4.
OR
2 (a) Find the probability of getting a sum of 10 if we throw two dice.
(b) A bag A contains 2 white and 3 red balls and a bag B contains 4 white and 5 red balls. One
ball is drawn at random from one of the bags and it is found to be red. Find the probability that
the red ball drawn is from bag B.
3 In a random sample of 60 workers, the average time taken by them to get to work is 33.8
minutes with a standard deviation of 6.1 minutes. Can we reject the null hypothesis ?? =32.6
minutes in favor of alternative null hypothesis ?? >32.6 and ?? =0.025 level of significance.
OR
4 A random sample of size 25 from a normal population has the mean ?? =47.5 and standard
deviation ?? =8.4. Does the information tend to support or refute the claim the mean of
population is ?? =42.5?
5 A tea company appoints four salesmen A, B, C and D and observe their sales in three
seasons- summer, winter and monsoon. The figures (in lakhs) are given in the below table.
Seasons
Sales men
Seasons total
A B C D
Summer 36 36 21 35 128
Winter 28 29 31 32 120
Monsoon 26 28 29 29 112
Sales totals 90 93 81 96 360
(i) DO the salesmen significantly differ in performance?
(ii) Is there significant difference between the seasons?
OR
6 To assess the significance of possible variation in performance in a certain test between the
convent schools of a city, a common test was given to a number of students taken at random
from fifth class of each of the four schools concerned. The results are given below. Make
analysis of variance of data.
Schools
A B C D
8 12 18 13
10 11 12 9
12 9 16 12
8 14 6 16
7 4 8 15
Contd. in page 2
Page 1 of 2
Code: 17FBS101
7
In a glass factory the task of quality control was done with the help of means ? ?? ? and standard
deviation ( ?? ) charts. 18 samples of 10 items each were chosen and ? ?? and ? ?? were found to
be 595.8 and 8.28 respectively. Determine 3?? limits for mean and standard deviation charts.
You may use the following control factors for your calculation.
N A1 B2 B4
10 1.03 0.28 1.72
OR
8 Construct a control chart for the proportion of defectives obtained in repeated random samples
of size 100 from a process which is considered to be under control when the proportion of
defective p is equal to 0.20. Draw the control line and the upper and lower control limits.
9 Calculate the coefficient of correlation between ?? and ?? .
X 1 2 3 4 5 6 7 8 9
Y 12 11 13 15 14 17 16 19 18
OR
10 Determine the equation of a straight line which best fits the data.
X 10 12 13 16 17 20 25
Y 10 22 24 27 29 33 37
*****
Page 2 of 2
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This post was last modified on 28 July 2020