To obtain revenue to support the funding of public educational programmes in
a city, the Parents and Teachers Association (PTA) proposes the establishment
of a City Football Lottery Programme (CFLP). The programme is to be
conducted on weekly basis for each of the 16 weeks which are played by the 20
teams in the Premier Football League. Suppose the PTA projects that on a
weekly basis the CFLP is expected to average Sh. 100,000 in profits with a
standard deviation of Sh. 2,500. Suppose further that the weekly profits data
are assumed to be (approximately) normally distributed.
Required:
(i) In the context of this problem, explain what the expected weekly average
profits of Sh. 100,000 with a standard deviation of Sh. 2,500 mean.
(3 marks)
(ii) If the PTA wanted to raise Sh. 200,000 on the average. Would they
manage to raise this amount through the CFLP? What is the expected
probability of raising this amount?
(6 marks)
(iii) Determine the interquartile range in weekly profits expected from the
CFLP.
(4 marks)