BCS-040
1. If 
= mean of set n observations i.e., x1, x2,…..,
xn, σx =
standard deviation of set of n observations. Similarly 
& σY are mean and standard deviation of set of
m observations. Show that standard deviation of pooled set x1, x2,
…. xn, y1, y2,
…. , ym for n + m observation is (5 Marks)
= mean of set n observations i.e., x1, x2,…..,
xn, σx =
standard deviation of set of n observations. Similarly & σY are mean and standard deviation of set of
m observations. Show that standard deviation of pooled set x1, x2,
…. xn, y1, y2,
…. , ym for n + m observation is (5 Marks)
2. Consider
a family with 2 children. Assume each child is as likely to be a boy as it is
to be a girl. What is the conditional probability that both children are boys
given that (i) the elder child is a boy (ii) at least one of the children is a
boy. (5 Marks)
3. It
has been claimed that in 60% of all Android Applications installation, the
utility bill is reduced by at least one third. Accordingly, what is the
probability that the utility bill we reduced by one third in (i) four of five
installations (ii) at least four of five installations. (5 Marks)
4. If
a Hardware support centre receives on an average λ = 6 wrong complaints per
day, then what is the probability that it will receive 4 wrong complains on any
given day. (5 Marks)
5. Verify
whether the following situations can be described by uniform distribution or
not. (i) The average life span of a bulb produced by manufacturing company,
(ii) the number of defective items produced by assembly process.
6. An
individuals IQ score has N(100, 152) distribution. Find the
probability that the individuals IQ score is between 91 and 121. (5 Marks)
7. From
a population of 200 observation, a sample of n = 50 is selected. Calculate the
standard error, if the population standard deviation equals 22. (5 Marks)
8. A
random sample of 100 observations is taken from a normal population having
variance σ2 = 42.5. Find the approximate probability of obtaining a
sample standard deviation between 3.14 and 8.94. (5 Marks)
9. If
independent random samples of size n1 = n2 = 8 comes from
normal populations having the same variance, what is the probability that
either sample variance will be at least seven times as large as the other ? (5
Marks)
10. A
random sample of 800 computers contains 24 defective items. Compute 99%
confidence interval for the proportion of defective computers. (5 Marks)
11. An
Antivirus developer claims that it cleans the entire system is 5 minutes (with
standard deviation of 2 minutes ). Ten people volunteers to take it to test the
claim. The average time to get the system cleaned was 7.5 minutes. Do you
accept the claim at 10 % level. (5 Marks)
12. A random
sample of size 1000 from lot of computers supplied by manufacture - 1, contains
20 defectives and a random sample of size 1500 from computers supplied by
manufacture - 2 contains 40 defectives. If α = 0.05, can you say computers
supplied by manufacture -1 are better than those supplied by manufacturer -2. (5 Marks)
13. A software
company owner has 3 developers A, B and C. During a particular week, the owner
tried to evaluate the productivity of A, B and C (x software developer was on
leave) (5 Marks)
|
Day ®
Developer ↓
|
1
|
2
|
3
|
4
|
5
|
|
A
|
6
|
8
|
6
|
5
|
*
|
|
B
|
7
|
8
|
7
|
5
|
8
|
|
C
|
9
|
8
|
*
|
6
|
*
|
Prepare a summary table, present the ANOVA table and
test (at 5 % level) whether all three (A, B, & C) are equally productive or
not.
14. An
economist wants to estimate relationship in a small community between a
family’s annual income & amount that family serves. Following data of 9
families obtained.
|
Annual income (thousand
dollar)
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
20
|
|
Annual savings (thousand
dollar)
|
0
|
0.1
|
0.2
|
0.2
|
0.5
|
0.5
|
0.6
|
0.7
|
0.8
|
Calculate
the least square regression line. 15. (5
Marks)
15. Fit
the trend curve to the population data given below, using second degree
equation, i.e., Tt = a0 + a1t +a2t2.
Use t = 1, 2, …., 10. How good is your fit. (5 Marks)
|
Census
|
2001
|
2002
|
2003
|
2004
|
2005
|
2006
|
2007
|
2008
|
2009
|
2010
|
|
UP Population (100002)
Crores
|
1906
|
2144
|
2142
|
2420
|
2729
|
3111
|
3598
|
4350
|
5355
|
6651
|
16. A sample of size 4 is to be selected from a population
of 11 computer brands. List all the possible sample by (i) Linear systematic
sampling (ii) circular systematic sampling. (5 Marks)
****************************************************************
Note: Answer
with Dotcom Books
www.dotcombooks4u.com
(Last 5 year
solved question paper with Assignment solutions)
9825183881
***************************************************************
No comments:
Post a Comment