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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]

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]

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