MA22S6 Numerical and Data Analysis 1 2015-2016
Homework sheet 3
Due Thursday 18th of February 2016 in class
Justify your answers with a few words, in particular when using a formula.
1. Out of ca. 30 hurricanes, a certain area of the eastern United states is, on the
average, hit by 6 hurricanes a year. What is the probability that during a certain
year, this area is hit
a) by fewer than four hurricanes;
b) by between five and eight hurricanes .
How large is the difference in the respective probabilities if one assumes a Poisson
distribution compared to the binomial distribution?
2. Suppose the probability that an item produced by a certain machine will be defective is 0.1. Assuming that the quality of successive items is independent, find
the probability that a sample of 10 items will contain at most one defective item.
Compare the results obtained with the binomial distribution to the one obtained
with the Poisson distribution.
3. We consider the binomial distribution with parameters n = 8, the number of trials
and p = 0.2, the probability that the outcome of each trial is “true”.
a) Graph the probability distribution, i.e. P (X = k) vs. k for k = 0, 1, 2, . . . 8.
b) Graph the corresponding Poisson distribution.
4. The label on a certain brand of syrup states that it is 99% pure maple syrup. In
fact, the percentage of pure maple syrup in any given bottle of this brand is a
uniform random variable X with values ranging from 98.5 to 99.5. What is the
probability that a bottle of this brand is
a) less than 99% pure maple syrup ?
b) more than 99.4% pure maple syrup ?
c) exactly 99% pure maple syrup ?
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Lecturer: Stefan Sint, sint@maths.tcd.ie
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