Chapter 11, Problem 35E

To determine

To Explain: that it is unusual for researcher to make six or greater shots in a row during a game.

Explanation of Solution

There is required to find the hot hand and, using the following measures, it can simulate:

Step 1

Each shot is a part.

Step 2

There is required to produce the random digits 00-99 for simulation. Let 01-65 stand for shots made and 66-99 and 00 missed shots.

Step 3

The test is made up of 20 simulated shots.

Step 4

Whether or not the 20 simulation shots contained a run of 6 or more insane shots is the answer component.

Phase 5 — Step 5

There is required to run at least 10 trials of the simulation process. By using random number generators, it produces random numbers using the following steps:

1) As per our needs, add random numbers.

2) Between 00 and 99, random digits are based on

3) Press the Submit key.

Trial Number	Component Outcomes	All Shots
1	66, 02, 76, 47, 03, 41	Yes
2	85, 34, 21, 46, 67, 49, 20, 41, 74, 74, 14	No
3	74, 96, 01, 23, 75, 93, 72, 15, 45, 13	No
4	23, 76, 01, 51, 90, 94, 87, 34, 93, 72, 15, 45, 13, 47, 71	No
5	95, 74, 75, 07, 40, 83	Yes
6	05, 00, 69, 05, 31, 23, 76, 01, 51, 90, 94, 87	No
7	79, 48, 81, 21, 12, 90	Yes
8	98, 41, 34, 21, 79, 48, 81, 21, 12, 90, 28, 23, 76, 01	No
9	00, 12, 95, 27, 72, 85	Yes
10	03, 51, 95, 21	No
Total		No

Let 01-65 stand for shots made and 66-99 and 00 missed shots. For instance, Trial number 1 shows the shots made, as up to 10 trials are within the range of 01-65 and so on.

Step 6

The percentage of which player shot is: There is required to find simulated

  $\begin{array}{c}Playermadeshot=\frac{totalnumberofsuccess}{totalnumberoftrials}\times 100\\ =\frac{4}{10}\times 100\\ =40\%\end{array}$

The percentage of players shot is 40%.

Phase 7 — Step 7

Based on the simulation, we can infer that the player is supposed to make six runs or more shots in a row, which is not unusual for 40 percent of games.