Apps. and Interpretation for IBDP Maths Ebook 1 | Page 357

2. In an office, Hoang is recording the number of free lunches offered by the external
sponsorships for staffs of different positions in the office in a particular working year.
The following table shows the distribution of the results for 100 staffs:
Number
of free
lunches
Adminstration
Positions
Customer
Service
Human
Resources
Others
0 4 4 20 6
1 3 6 5 20
2 2 10 2 2
3 or more 1 10 3 2
A
2
� test for independence is conducted at a 5% significance level.
(a) (i) Write down the null hypothesis of the test.
(ii) Write down the alternative hypothesis of the test.
(b) Write down the degree of freedom of the test.
(c) Find the p -value.
(d) Write down the value of �
2
calc
, the test statistic.
(e) State the conclusion of the test with a reason.
One staff is selected at random.
[2]
[1]
[2]
[1]
[2]
(f) (i) Find the probability that the staff is from the customer services department
and is not offered any free lunch.
(ii)
Find the probability that the staff is offered at least two free lunches.
23
(g)
(iii)
Given that the staff is offered two free lunches, find the probability that
the staff is from the administration department.
Two staffs are selected at random. Find the probability that both of them are
offered at most one free lunch.
[6]
[3]
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