# (7 pages) APRIL 2013 12. What is the difference between small sample and

```(7 pages)
APRIL 2013
12. What is the difference between small sample and
large sample?
Answer any TEN questions each in 50 words.
All qu~tions carry equal marks.
4.
Defineprol;Jability.
13. A retailer purchases berries every· morning at
Rs. 5 a case and sells for Rs. 8 a case. Any case
remaining unsold at the end of the day can be
disposedof next day at a salvage value of Rs. 2 per
case (thereafter they have no value). Past sales
have ranged from 15 to 18 cases per day.
The folloWing is the record of sales for Past
120 day:
Cases sold: 15 16 17 18
No~of days: 12 24 48 36
Find how many cases the retailer should purchase
Per day to maximise his pmfit.
14.
15.
16.
Three groups of workers contain 3 men and one
woman, 2 men and 2 women, and 1 man and three
women respectively. One worker is selected at
random from each group. What is the probability
that the group selected consist of 1 man and
2 women?
regulators,
r12= 0.70; rta = 0.61; 1'28= 0.40.
assembly
electrical
of which is being
space and finance, the number of workers
employed cannot exceed 11 and their salary bill
not more than Rs. 6000 per month. The. male
members ()f the skilled workers are paid Rs. 600
per month, while the female worker, doing the
same work as the male member gets Rs. 500 per
month. Data collected on the performance of these
workers indicate that a male member contributes
Rs. 1000 per month to total return of the industry,
A random sample of size 16 has 53 as mean. The
sum of the squares of the deviations taken from
mean is 135. Can this ~ple
be regarded as
taken from the ,population having 56 as mean?
Obtain 95% and 99% confidence limits of the mean
of the population.
On the basis of the following information compute:
(a) 1'28.1
(b) rl3.2and (c) rt2.8:
the
manufactures
accomplished by a small group of skilled workers,
both men and women .. Due to the limitations of
Assuming that half the population is vegetari.all
so that the chance of an individual being
a vegetarian
IS
~
and assuming that
100
investigators
can
take
sample
of
10 Individuals to see whether they are
vegetarians, how many investigators would you
expect to report that three people or less were
vegetarians?
(for v = 15, to.05= 2.13 for v = 15, to.Ol= 2.95).
17.
18. A small scale industry
while the female worker contributes' Rs. 850 per
month. Formulate the LPP to determine the
number of male and female workers to be
employed in order to maximize the monthly total
return.
19.
Assume the mean height of soldiers to be
68.22 inches with a variance of 10.8 inches. How
mapy soldiers in a regiment of 1,000 would you
expect is being over six feet tall?
6S1071KCA2B
[p.T.O.]
Calculate the Karl Pearson's coefficient of
correlation from the followingdata and interpret
its value:
Marks in Accountancy: 48 35 17 23 47
Marks in Statistics:
45 20 40 25 45
The customer accounts at a certain departmental
store have an average balance of Rs. 480 and a
standard deviation of Rs. 160. Assuming that the
account balances are normally distributed.
(a) What proportion of· the accounts is over
Re.OOO?
(b) What proportion of the accounts is between
Rs. 400 and Rs. 6OO?
(c) What proportion of the accounts is between
Re. 240 and Rs. 360?
A manufacturing company has purchased three
new machines of different makes and wishes to
determine whether one of them is faster than the
others in producing a certain output. Five hourly
production figures are observed at random from
each machine and the results are given below:
1
25 31 24
2
30 39 30
3
36 38 28
Use the analysis of variance and determine
whether the machines are significantly different.
in their mean speed. (Given at 5% Level
F2.12 = 3.89).
25.
Eight coins are tossed at a time 25_6times.
Number of heads observed at each throw is
recorded and the results are given below.Find the
expected frequencies. What are the theoretical
values of mean and standard deviation? Calculate
also the mean and S.D.of the frequencies.
No. of heads at a throw:
0
1
2
3
4
5 ~. 7 8
Frequency :
2
6
30
52 67 56 32 10 1
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