Q.1. There
is this disease which is extremely dangerous.
Only 0.1% of the population has this disease. A test has been developed to detect a
disease. Among the diseased population, the test gives a positive result in 99%
of the cases. Among the healthy
population, the test gives a negative result in 99.5 % of cases. Therefore,
this test is very effective among the diseased population and healthy
population.
Kumar is concerned since
many of his family members have contracted the disease and died. He decided to take the test. He has decided that if the probability that
he has the disease is at least 20%, he will resign his job, cash all his
savings and enjoy while it lasts!
Otherwise he will sit tight and wait for further developments. He takes the test and the result is
positive. Use what you have learnt in
this course (till midterm) and advise Kumar.
[5]
Q.2. The following
contingency table gives the relationship between a man’s age and his job grade
in a large industrial area. Each job has
a grade reflecting the value of that job to the firm and the table has been
generated from a sample of industrial workers.
Job
Grade 
Age 

Young 
MiddleAge 
Old 

1 
60 
880 
60 
2 
240 
3530 
230 
An employee
is selected at random.
(a)
Compute
the probability that he is young.
(b)
Compute
the probability he is young given that he is in Job Grade 1.
(c)
What
can you infer from the computations of the marginal and conditional
probabilities? [1 + 1 + 2 = 4]
Q.3.
The number of patients consulting the village doctor on any day is
a random variable with μ = 18 and σ = 2.5.
Use Chebyshev’s Theorem to estimate the probability that on a random day,
the number of visitors will be between 8 and 28. [2]
Q.4.
The population has Q1 = 42, Q2 = 44 and Q3 = 50. From this limited information, do you think
the distribution of the data is left skewed, right skewed or symmetric? Explain your inference. [2]
Q.5.
The life expectancy of an electronic item is normally
distributed with a mean of 4 years and a standard deviation of 1 year. How many years should this item last at a
minimum, so that it is in the top 5% of the population? [3]
Q.6.
A primary health center
health center reported that in a sample of 400 patients 80 had severe
fever. The director of health has asked
you to compute a 90% confidence interval for the population proportion with
severe fever.
(a)
Compute the required confidence interval. Your answer should follow the logical
sequence as done in class.
Incidentally the 95% confidence
interval is (0.1608, 0.2392).
(b)
Explain why the 95% confidence interval will be larger than the
90% confidence interval.
(c)
The Director went and told the minister that the probability that
the disease rate is between 16.08% and 23.92% is 0.95. Explain (briefly)
why this is nonsensical!
[5 + 1 + 2 = 8]
Q.7.
The furniture company promises to fulfill your order within 15
days of purchase. A sample of 49 past customers is taken. The average delivery
time in the sample was 16.2 days with a samplestandard
deviation of 5.6 days. Test the promise
at 1% significance level. Use the
Critical Value approach.
Your answer should follow
the logical sequence as done in class. [6]
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