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## Statistics and probability

### Course: Statistics and probability>Unit 6

Lesson 2: Sampling and observational studies

# 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 2 lines of random digits we'll use in this worksheet:
Line 1: 9656505007166058119414873041978557645195
Line 2: 1116915529332418359401727865956572382322
Things to know about random digit tables:
• Each digit is equally likely to be any of the 10 digits 0 through 9.
• 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 5 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 90 students in a lunch period, and 5 of them will be selected at random for cleaning duty every week. Each student receives a number 01, minus, 90 and the school uses a random digit table to pick the 5 students as follows:
• Start at the left of Line 1 in the random digits provided.
• Look at 2-digit groupings of numbers.
• If the 2-digit number is anything between 01 and 90, that student is assigned lunch duty. Skip any other 2-digit number.
• Skip a 2-digit number if it has already been chosen.
Line 1: space, 9656505007166058119414873041978557645195
Which 5 students should be assigned cleaning duty?

## Problem 2: Doing a simulation

A cereal company is giving away a prize in each box of cereal and they advertise, "Collect all 6 prizes!" Each box of cereal has 1 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 6 prizes.
She decides to do a simulation using random digits as follows:
• Start at the left of Line 2 in the random digits provided.
• Look at single digit numbers.
• The digits 1, minus, 6 represent the different prizes.
• She ignores the digits 0, comma, 7, comma, 8, comma, 9.
• One trial of the simulation is done when all 6 digits have appeared.
• At the end of the trial, she counts how many digits it took for every digit 1, minus, 6 to appear (ignoring the other digits).
Line 2: space, 1116915529332418359401727865956572382322
question a
How many boxes of cereal did it take to get all 6 prizes?
boxes

question b
Caroline did some more trials of her simulation. Each trial, she recorded how many boxes it took to get all 6 prizes. Her results are shown in the table below.
Trial #Number of boxes
112
217
315
47
520
On average, how many boxes of cereal did it take Caroline to get all 6 prizes?