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02000M A206052004
PART B
Answer any two full questions, each carries 15 marks.
The population consisting of 5 members 2, 3, 6, 8, 11. Consider all possible distinct
samples of size 2 with replacement. Find the population mean , mean of the sampling
distribution of mean and the standard deviation of the sampling distribution of mean.
The time at the counter for a customer to be served at a post office can be modelled as
a random variable having mean = 176 seconds and variance = 256 seconds. The
sample mean X will be obtained from the times for a random sample of 100
customers. What is the probability, using central limit theorem, that X will be
between 175 and 178 seconds?
The specification for certain kind of ribbon call for a mean breaking strength of 180
Pounds. If five pieces of ribbon have a mean breaking strength of 169.5 pounds with
a standard deviation of 5.7 pounds, test the null hypotheses ൮൦180 pounds against the
alternative hypotheses ‏ير‎ > 180 pounds at 1% level of significance. Assume the
population distribution is normal.
A stenographer claims that she can take dictation at the rate of 120 words per minute
can we reject her claim on the basis of 100 trials in which she demonstrate a mean of
116 words with standard deviation of 15 words. (Use 5% level of significance)
The mean operating life of a random samples of 15 bulbs taken from a population
with standard deviation 500 hrs 15 8900 hours Find,
i) 95% confidence level
ii) 90% confidence level for the population mean
To test the claim that the resistance of an electric wire can be reduced by more than
0.05 ohms by allowing 32 values obtained for a sample wire yielded x; =0.136 ohms
and S,;=0.004 ohms and 32 values obtained for alloy wire yielded Xz =0.083 ohms
and S2=0.005 ohms at 0.05 level of significance, Does this support the claim ?
PART C

Answer any two full questions, each carries 20 marks.

Use Lagrange’s formula to find the value of y at x = 6 from the following data

y 168 120 72 63

Using Newton - Raphson Method compute the V51 correct to 4 decimal places.

Using Newton’s forward interpolation formula, find the value of sin52°, given that

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