19-01-2013, 12:46 PM
PROBABILITY AND STATISTICS Bio-Technology Answer any FIVE Questions
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1. (a) In a certain factory there are two independent processes for manufacturing the
same item. The average weight in a sample of 250 items produced from one
process is found to be 120 gms with a standard deviation of 12 gms while the
corresponding gures in a sample of 400 items from the other process are 124
and 14. Is there signicant dierence between the mean (test at 95% level).
(b) A sample of 1000 products are examined from a factory and 2.5% found to
be defective. Another sample of 1500 similar products are examined and 2%
found to be defective. Test the signicance between the dierence of two
proportions at 5% level. [8+8]
2. (a) What is the maximum error one can expect to make with probability .95,when
using the mean of a random sample of size n=90 to estimate the mean of a
population with 2 = 6.25
(b) A sample of 155 members has a mean 67 and S.D 5.2. Is this sample has been
taken from a large population of mean 70?
© A random sample of 400
ower stems has an average length of 15 cms. Can
this be regarded as a sample from a large population with mean 16 cms and
standard deviation 5 cms.? [5+5+6]
3. A typist at an oce receives on average 30 letters per day for typing. The typist
works 8 hours per day and he takes 15 minutes for typing
(a) What is the average number of letters waiting to be typed?
(b) The probability that more than or equal to 4 letters are being waiting to be
typed.
© What is the average waiting time needed to have a letter to be typed?
(d) The time that the typist is idle per day [16]
4. (a) Find the Mode of Poisson Distribution.
(b) In a distribution exactly normal 7% of the items are under 35 and 89% are
under 63. nd the mean and the Standard deviation of mark