Apps. and Interpretation for IBDP Maths Ebook 1 | Page 356

Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 99
1. In order to improve the service, the manager of a bus company is investigating the
number of on time arrivals and late arrivals of buses in four different bus stations. The
manager wants to know whether there is an association between the punctuality of buses
and the locations of bus stops.
The following table shows the distribution of the 100 bus arrivals in different bus
stations:
Arrivals
Bus stations
A B C D
On time 19 17 20 29
Late 1 3 8 3
A
2
� test for independence is conducted at a 10% 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 value of �
2
calc
, the test statistic.
The critical value is given by 6.251.
(d) State the conclusion of the test with a reason.
One bus arrival record is selected at random.
[2]
[1]
[2]
[2]
(e) (i) Find the probability that the arrival record is on time and at the bus station
C.
(ii)
Find the probability that the arrival record is late.
(f)
(iii) Given that the arrival record is on time, find the probability that the arrival
record is at the bus station A.
[6]
Two bus arrival records are selected at random. Find the probability that both of
them are on time.
[3]
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