Descriptive Statistics
Tutorial Sheet 4
1. In a medium-sized firm, the number of absent workers on a particular day has
a Poisson distribution with mean 4. Calculate the probability that on a given
day
i)
no-one is absent.
ii)
at least 3 people are absent.
iii)
between 4 and 6 (inclusively) people are absent.
2. In a newspaper on average 1 in 10 000 characters is incorrectly printed.
Suppose the paper contains 50 000 characters.
a) Calculate the exact probability that
i)
no printing errors are made
ii)
at least 3 errors are made
b) Using the appropriate approximation, estimate these two probabilities.
3. A die is rolled until the first number divisible by 3 appears. Calculate the
probability that
i)
the die is rolled exactly once
ii)
the die is rolled exactly four times
iii)
the die is rolled at least four times
iv)
the number of rolls is even.
4. In the European lottery 6 numbers are chosen without replacement from 49.
Calculate the probability of
i)
winning the jackpot (choosing all 6 numbers correctly)
ii)
winning the smallest prize (choosing 3 of the 6 numbers
correctly)
iii)
choosing at least one of the numbers correctly.
5. A computer chooses a number at random n times from the set {1, 2, 3, 4, 5}
(with replacement). Let S denote the sum of the numbers chosen. Show that
E(S) = 3n and Var(S) = 2n.