1. For this assessment, explicityly state the five steps of a simulation and carry out the simulation. Use the random digit table.
A basketball player makes 80% of her free throws. Recently during a very close game, she shot 5 free throws near the end of the game and missed 3 of them. The fans booed. What is the probability of her missing 3 (or more) free throws out of 5? Set up and conduct a simulation (using the random digits below) with 10 repetitions.
83234602784360127630126087268768056651093246461081275417450
17491243217468017649817480716408712807408783402746237416207
48648148631085738
To find the probability of a basketball player missing 3 (or more) free throws out of 5, we can set up a simulation using the given random digit table. Here are the five steps of a simulation:
Step 1: Identify the event and determine the outcome of interest.
In this case, the event is shooting 5 free throws, and the outcome of interest is missing 3 (or more) of them.
Step 2: Assign random digits to represent the outcomes.
Assign the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 to each possible outcome.
Step 3: Generate random numbers using the random digit table.
Starting at the beginning of the table, read the digits in groups of two, four, or five depending on the number of free throws attempted.
Step 4: Interpret the random numbers and determine the outcome.
Use the generated random numbers to determine if each free throw is a miss or a make. If the random number is less than or equal to 2 (or any other predetermined cutoff point), consider it a missed free throw. Otherwise, consider it a made free throw.
Step 5: Repeat steps 3 and 4 multiple times to simulate the event.
Repeat the process multiple times (in this case, 10 repetitions) to simulate the event and obtain a sample of outcomes.
Now, let's carry out the simulation using the provided random digit table:
Simulation:
Repetition 1:
Random numbers: 83, 23, 46, 02, 78
Outcome: Make, Make, Miss, Miss, Make
Number of missed free throws: 2
Repetition 2:
Random numbers: 34, 60, 12, 76, 30
Outcome: Miss, Miss, Make, Miss, Miss
Number of missed free throws: 4
Repetition 3:
Random numbers: 12, 60, 87, 68, 68
Outcome: Miss, Miss, Miss, Miss, Miss
Number of missed free throws: 5
Repetition 4:
Random numbers: 56, 65, 10, 93, 24
Outcome: Make, Make, Miss, Make, Miss
Number of missed free throws: 2
Repetition 5:
Random numbers: 17, 49, 12, 43, 21
Outcome: Miss, Miss, Miss, Miss, Miss
Number of missed free throws: 5
Repetition 6:
Random numbers: 17, 68, 01, 76, 41
Outcome: Miss, Miss, Miss, Miss, Miss
Number of missed free throws: 5
Repetition 7:
Random numbers: 48, 64, 81, 48, 63
Outcome: Make, Make, Make, Make, Miss
Number of missed free throws: 1
Repetition 8:
Random numbers: 10, 85, 73, 80, 74
Outcome: Miss, Miss, Make, Make, Make
Number of missed free throws: 2
Repetition 9:
Random numbers: 87, 83, 40, 27, 46
Outcome: Make, Make, Make, Make, Miss
Number of missed free throws: 1
Repetition 10:
Random numbers: 37, 41, 62, 37, 41
Outcome: Miss, Miss, Make, Miss, Miss
Number of missed free throws: 3
From the 10 repetitions, we can observe that the number of missed free throws varies. Now, we can calculate the probability of missing 3 (or more) free throws out of 5 by finding the proportion of repetitions where the number of missed free throws is 3 or greater.
Out of the 10 repetitions, there are 2 repetitions where the number of missed free throws is 3 or greater (Repetition 2 and Repetition 10).
Therefore, the probability of the basketball player missing 3 (or more) free throws out of 5 based on this simulation is 2/10 or 0.2.