Simulation and randomness: Random digit tables

We can simulate events involving randomness like picking names out of a hat using tables of random digits. Tables of random digits can be used to simulate a lot of different real-world situations. Here's 22 lines of random digits we'll use in this worksheet:
Line 11: 965650500716605811941487304197855764519596565\,\, 05007\,\, 16605\,\, 81194\,\, 14873\,\, 04197\,\, 85576\,\, 45195
Line 22: 111691552933241835940172786595657238232211169\,\, 15529\,\, 33241\,\, 83594\,\, 01727\,\, 86595\,\, 65723\,\, 82322
Things to know about random digit tables:
  • Each digit is equally likely to be any of the 1010 digits 00 through 99.
  • The digits are independent of each other. Knowing about one part of the table doesn't give away information about another part.
  • The digits are put in groups of 55 just to make them easier to read. The groups and rows have no special meaning. They are just a long list of random digits.

Problem 1: Getting a random sample

There are 9090 students in a lunch period, and 55 of them will be selected at random for cleaning duty every week. Each student receives a number 019001-90 and the school uses a random digit table to pick the 55 students as follows:
  • Start at the left of Line 11 in the random digits provided.
  • Look at 22-digit groupings of numbers.
  • If the 2-digit number is anything between 0101 and 9090, that student is assigned lunch duty. Skip any other 22-digit number.
  • Skip a 22-digit number if it has already been chosen.
Line 11:  9656505007166058119414873041978557645195~96565\,\, 05007\,\, 16605\,\, 81194\,\, 14873\,\, 04197\,\, 85576\,\, 45195
Which 55 students should be assigned cleaning duty?
Choose 1 answer:
Choose 1 answer:

Problem 2: Doing a simulation

A cereal company is giving away a prize in each box of cereal and they advertise, "Collect all 66 prizes!" Each box of cereal has 11 prize, and each prize is equally likely to appear in any given box. Caroline wonders how many boxes it takes, on average, to get all 66 prizes.
She decides to do a simulation using random digits as follows:
  • Start at the left of Line 22 in the random digits provided.
  • Look at single digit numbers.
  • The digits 161-6 represent the different prizes.
  • She ignores the digits 0,7,8,90, 7, 8, 9.
  • One trial of the simulation is done when all 66 digits have appeared.
  • At the end of the trial, she counts how many digits it took for every digit 161-6 to appear (ignoring the other digits).
Line 22:  1116915529332418359401727865956572382322~11169\,\, 15529\,\, 33241\,\, 83594\,\, 01727\,\, 86595\,\, 65723\,\, 82322
question a
How many boxes of cereal did it take to get all 66 prizes?
boxes
question b
Caroline did some more trials of her simulation. Each trial, she recorded how many boxes it took to get all 66 prizes. Her results are shown in the table below.
Trial #Number of boxes
111212
221717
331515
4477
552020
On average, how many boxes of cereal did it take Caroline to get all 66 prizes?
If necessary, round your answer to the nearest tenth.
boxes
question c
Caroline's friend Grant did his own simulation. He did his just like Caroline, but he did 2020 trials instead of 55. On average, it took him 14.814.8 boxes to get all 66 prizes.
Whose results are more likely to give a closer estimate to the true average number of boxes it takes to get all 66 prizes?
Choose 1 answer:
Choose 1 answer:
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