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Definitions
FR # 1
Simulation
Simulation of random events
Calculator
100
An event that we know what outcomes could happen, but not which particular values will happen.
What is Random?
100
Joey is interested in investigating so-called hot streaks in foul shooting among basketball players. He’s a fan of Carla, who has been making approximately 80% of her free throws. Specifically Joey wants to use simulation methods to determine Carla’s longest run of baskets on average, for 20 consecutive free throws. a) Describe a correspondence between random digits from the RDT and outcomes.
Let make = 0-7 and miss =8, 9
100
On average, suppose a baseball player hits a home run once in every 10 times at bat, and suppose he gets exactly two "at bats" in every game. Using simulation, estimate the likelihood that the player will hit 2 home runs in a single game. 1.) Describe the possible outcomes. For this problem, there are two outcomes
the player hits a home run or he doesn't.
100
1.Describe the possible outcomes. 2.Link each outcome to one or more random numbers. 3.Choose a source of random numbers. 4.Choose a random number. 5.Based on the random number, note the "simulated" outcome. 6.Repeat steps 4 and 5 multiple times; preferably, until the outcomes show a stable pattern. 7.Analyze the simulated outcomes and report results.
What is the steps required to run a simulation?
100
entering a command that would generate 10 numbers at a time from 0 - 99
What is the calculator command "ranInt (0, 99, 10) "
200
This models random events by using random numbers to specify event outcomes with relative frequencies that correspond to the true real-world relative frequencies we are trying to model.
What is Simulation?
200
Joey is interested in investigating so-called hot streaks in foul shooting among basketball players. He’s a fan of Carla, who has been making approximately 80% of her free throws. Specifically Joey wants to use simulation methods to determine Carla’s longest run of baskets on average, for 20 consecutive free throws. b) What will constitute one repetition in this simulation?
“Shoot” 20 shots by looking at 20 random digits and count the longest run of makes.
200
On average, suppose a baseball player hits a home run once in every 10 times at bat, and suppose he gets exactly two "at bats" in every game. Using simulation, estimate the likelihood that the player will hit 2 home runs in a single game. Link each outcome to one or more random numbers. Since the player hits a home run in 10% of his at bats, 10% of the random numbers should represent a home run.
let's say that the digit "2" represents a home run and any other digit represents a different outcome.
200
One event has no effect or influence over the next (e.g. coin tosses).
What is Independent?
200
a formula in which creates values
What is pseudo-random?
300
The most basic situation in a simulation in which something happens at random.
What is Simulation Component?
300
Joey is interested in investigating so-called hot streaks in foul shooting among basketball players. He’s a fan of Carla, who has been making approximately 80% of her free throws. Specifically Joey wants to use simulation methods to determine Carla’s longest run of baskets on average, for 20 consecutive free throws. c) Starting with line 101 in the random digit table, carry out 10 repetitions and record the longest run for each repetition.
Starting at Line 101, we have the following random digits for the first repetition of 20 shots:
300
On average, suppose a baseball player hits a home run once in every 10 times at bat, and suppose he gets exactly two "at bats" in every game. Using simulation, estimate the likelihood that the player will hit 2 home runs in a single game. 3) perform a simulation using a calculator to generate random numbers to conduct 10 trials.
*students should know how to operate the calculator*
300
Choose a person at random from a group of which 70% are employed. One digit simulates one person.
For example: 0, 1, 2, 3, 4, 5, 6 = employed 7, 8, 9 = not employed
300
Creates the random numbers based upon its seed.
What is seeding a calculator?
400
an individual result of a component of a simulation
What is Outcome?
400
Joey is interested in investigating so-called hot streaks in foul shooting among basketball players. He’s a fan of Carla, who has been making approximately 80% of her free throws. Specifically Joey wants to use simulation methods to determine Carla’s longest run of baskets on average, for 20 consecutive free throws. Explain a method joey could use to simulate Carla's longest run of baskest. d) What is the mean run length for the 10 repetitions?
1.) use a random generator or random table. 2.) let make = 0 - 7 and miss = 8, 9 3.) analyze single digits at a time. 4.) conclusion
400
On average, suppose a baseball player hits a home run once in every 7 times at bat, and suppose he gets exactly two "at bats" in every game. Using simulation, estimate the likelihood that the player will hit 5 home runs in a single game. ) Explain how you would simulate this situation
*answer varies*
400
Choose one person at random from a group of 73% are employed. Now two digits simulate one person:
For example: 00, 01, 02, . . . . , 72 = employed 73, 74, 75, . . . . , 99 = not employed
400
entering a command that would generate 3 numbers at a time from 0 - 45
What is the calculator command "randInt(0,45,3)"?
500
The sequence of several components representing events that we are pretending will take place.
What is Trial?
500
Using a calculator, generate 100 numbers and to 10 trials to simulate the situation
*answer varies* teacher please check ( 10 min)
500
Studies has shown that the probability of having a boy is .35, and the probability of having a girl is .65. Explain how to conduct this simulation with a total of ten trials
Let boy = 0 - 34 and girl = 35 - 99 . Analyze two digits at a time until we get 10 trials. ( sets of two-digits varies)
500
Choose one person at random form a group of which 50% are employed, 20% are unemployed, and 30% are not in the labor force. There are now three possible outcomes, but the principle is the same. One digit simulates one person:
For example: 0, 1, 2, 3, 4 = employed 5, 6 = unemployed 7, 8, 9 = not in the labor force
500
entering a command that would simulate a coin toss with 10 trials.
What is the calculator command "randInt( 0,1)"