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Descriptive Statistics
Additional Sheet 6
1. The mean earnings of Poles are 2500 zl/month with a standard deviation of
1500zl/month. Using the central limit theorem, estimate the probability that the mean
monthly earnings of 100 randomly chosen Poles are
i)
greater than 2800 zl
ii)
between 2400 and 2600 zl.
2. Estimate the probability that the sum of 400 independent exponential random
variables with expected value 1 is between 370 and 410.
3. a) A die is rolled 180 times. Using an appropriate approximation, estimate the
probability that
i) exactly 26 sixes are thrown
ii) between 28 and 33 heads (inclusively) are thrown
4. The number of individuals who are on sick leave on a given day in a firm has a
Poisson distribution with mean 2. Assuming there are 250 working days in a year,
using the appropriate approximating distribution, estimate the probability that in the
course of a year there are
a) more than 550 working days lost due to illness
b) between 480 and 530 (inclusively) days lost to illness.