STAT 350 Assignment 4 Solutions
(70 points)
CHAPTER 5
1.
(a)
(3)
Sampling without replacement means that no repeated items will occur in any sample. There are 10
possible such samples of size 3:
{a,b,c}, {a,b,d}, {a,b,e}, {a,c,d}, {a,c,e}, {a,d,e}, {b,c,d}, {b,c,e}, {b,d,e}, {c,d,e}.
As you learned in the discussion of the binomial distribution, the number of ways to choose a sample of 3
distinct items from a list of 5 items is given by
3
5
= 10, which shows that the list above is indeed complete.
(b)
(2)
A contains 3 samples from the list in (a); i.e., A = { {a,b,c}, {a,c,d}, {a,c,e}}
(c)
(2)
The complement of A is A
=
{{a,b,d}, {a,b,e}, { {a,d,e}, {b,c,d}, {b,c,e}, {b,d,e}, {c,d,e}}
2.
A Venn diagram of these three events is
(a)
(2)
The event ‘at least one plant is completed by the contract date’ is represented by the shaded area covered
by all three circles:
(b)
(2)
The event ‘all plants are completed by the contract date’ is the shaded area where all three circles overlap:
(c)
(2)
The event ‘none of the plants is completed by the contract date’ is the complement of the shaded area in
(a).
(d)
(2)
The event ‘only the plant at site 1 is completed by the contract date’ is shown shaded:
(e)
(2)
The event ‘exactly one of the three plants is completed by the contract date is:
(f)
(2)
The event ‘either the plant at Site 1 or Site 2 or both plants are completed by the contract date’ is: