(b)

3. (a)

(b)

4. (a)

(b)

5. (a)

(b)

6. (a)

(b)

From the following data on age of employees, calculate the coefficient of skewness
and comment on the result:

(4.5 marks)
Distinguish between Exclusive type and Inclusive type class intervals. (3 marks)
Consider two different businesses with equal initial investment and equal lives, whose

expected cash flows (in Rs. crores) are summarized as follows. Identify the business
which is more consistent in terms of cash flow:

Period | 1 | 213141] 5 |
Business A | 80 | | 85 | 70 | 100 | | 115 |

| 100 | 70 [90 | 80 [150 |

(4.5 marks)
PARTB

In a normal distribution with mean 375 and standard deviation 48, how large a sample
must be taken so that the probability will be at least 0.95 that the sample mean falls
between 370 and 380? (3 marks)

Seven homemakers were randomly sampled, and it was determined that the distances
they walked in their housework had an average of 39.2 miles per week and a sample
standard deviation of 3.2 miles per week. Construct a 95% interval for the population
mean. (4.5 marks)

QC department of a paint manufacturing company, at the time of despatch of
decorative paints, discovered that 30 per cent of the containers are defective. If a
random sample of 500 containers is drawn with replacement from the population,
what is the probability that the sample proportion will be less than or equal to 25 per
cent defective? (3 marks)

Two independent samples of students representing Region 1 and Region 2 of a
program are taken from normal populations with the same variance. The variance of
marks of 16 students of a sample taken from the Region 1 is 225 and the variance of
marks of 12 students of another sample taken from the Region 2 is 144. Check
whether the variance of the marks of the first sample is less than the variance of the
marks of the second sample at a significance level of 0.01. (4.5 marks)

Illustrate multi-stage sampling with an example. (3 marks)

Two salesmen, A and B are working in a certain district. From a sample survey
conducted by the head office, following results were obtained. State whether there is
any significant difference in the average sales between the two salesmen. Take
a=0.05.

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