Analyzing Patterns with Random Numbers

[LAYAN-2008]

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The main aim of this question is to assess your understanding of the use of random numbers in analyzing patterns.

The table below gives the number of births on each day of a week in all maternity hospitals in a certain city.
Day Number of births
Sunday (day 1) 10
Monday (day 2) 6
Tuesday (day 3) 6
Wednesday (day 4) 13
Thursday (day 5) 5
Friday (day 6) 6
Saturday (day 7) 14

Suppose that births are equally likely to take place on each day of the week.
(a) Explain how you could use your calculator to generate random integers from 1 to 7. [3]
MATH-PRB-5:RANDINT(1,7)

(b) Use your calculator to generate 60 random integers from 1 to 7 and store them in a
list LI. Explain how you did this. [3]

MATH-PRB-randInt(1,7,60)-Sto-L1
(c) The numbers stored in LI provides a simulation of a random distribution of number
of births on each day of any week in which there are 60 births. Explain how the 60
numbers in the list should be interpreted in terms of such a simulation. [2]


(d) Sort the numbers in LI into ascending order, and hence locate the numbers which
occur more than once. Give the frequency of the occurrence of these numbers. [2]



(e) Does your simulation suggest that it is unlikely that 27 births take place on the same
day ? Explain why. [2]

 

[Valkarie]

No, the simulation does not suggest that it is unlikely that 27 births take place on the same day. This is because the number of births on each day could vary and it is possible that all the 60 births are distributed evenly across the 7 days, resulting in 27 births on a single day.