University of Phoenix - MBA
Question 1. Toss a coin 10 times and record the proportion of heads so far. Answer. Table for Head Proportion
H or T?
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)
Also INT(2 * 0.78934) INT(1.57868)
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.
Each time that a new set of random numbers is generated, the graph changes accordingly. However, in all of these graphs we can still see that the proportion of heads so far approaches the 0.5 value as the number of tosses increases. The following is one of the graphs obtained this way:
Answer 6: The following is a graph obtained with the simulation. As expected, the graph shows that the proportion of hits approaches 0.5 as the number of free throws increases. In the simulation, the first throw was a hit, which gave us a first proportion of 1.0. However, after that, we had a streak of misses that lower the proportion all the way to 0.40. By the time we got to throw 100, our proportion (the hits mean) was 0.47. Our longest streak of hits happened from throws #7 to #15, inclusive, for a streak length of 9. Our longest streak of misses happened from throws #72 to #77, inclusive, for a streak length of 6.
Answer 7: The graph obtained from the simulation appears next.
As the number of throws increases, the proportion of hits so far approaches 0.75, as expected. 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 increases.
The following frequency distribution reports the number of frequent flier miles, reported in thousands, for employees of Brumley Statistical Consulting, Inc., during the most recent quarter.
Frequent Flier Miles (000)
Number of Employees
0 up to 3
3 up to 6
6 up to 9
9 up to 12
12 up to 15
How many employees were studied?
Answer. A total of 50 employees were studied.
c. Construct a histogram.
Answer. The following graph is the histogram for the data given.
Chapter 3 Exercise 85
Answer A. The life expectancy data is shown next, sorted in ascending order:
United Arab Emirates
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