QRB/501

University of Phoenix - MBA

Activity 18:1:

Question 1. Toss a coin 10 times and record the proportion of heads so far.

Answer. Table for Head Proportion

Toss # 1 2 3 4 5 6 7 8 9 10

H or T? H T T H H H T T H T

Proportion 1/1 1/2 1/3 2/4 3/5 3/6 3/7 3/8 4/9 5/9

Question 2. Plot the proportion of heads so far, for each toss from the previous table. What does the graph show?

Answer. Shown below is the graph plotted in Excel worksheet showing the first toss of H and the proportion of toss 1 at 1.0 and the subsequent one as it increases getting to 0.5

Question 3 Answer.

Therefore INT(2 * 0.13061) INT(0.26122)

0

Also INT(2 * 0.78934) INT(1.57868) 1

Answer to Question 4. Graph from Excel

From the graph – it can be seen that as the tosses number increase, so also the head proportion moving toward 0.5 In our simulation, the first toss has an H, which we can see because the proportion starts at 1.0. Following the first simulated toss, the proportion changes with each new toss depending on whether we got an H or a T.

Answer 5

Each time that a new set of random numbers is generated, the graph changes accordingly. However, in all of these graphs we can

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The overall proportion of hits by throw 100 was 0.73. The longest streak of hits was from throws #87 to #98, inclusive, for a length of 12 consecutive hits. The longest streak of misses was from throws #55 to #60, inclusive, for a length of 6 consecutive misses. When compared against the previous simulation, the longest streak of hits was substantially longer; in the previous simulation we had Shaquille with a streak of 9 hits, while here we have a streak of 12 hits. For misses, in both cases the longest streak was of 6 misses. We can conclude that we’ll see longer streaks of hits as the probability of hits