Law of Large Numbers: Gambling Betty and Jane are gambling. They are cutting cards (picking a random place in the deck to see a card). Whoever has the higher card wins the bet. If the cards have the same value (for example, they are both eights), they try again. Betty and Jane do this a 100 times. Tom and Bill are doing the same thing but are betting only 10 times. Is Bill or Betty more likely to end having very close to 50% wins? Explain. You may refer to the graph to help you decide. It is one simulation based on 100 trials.
Law of Large Numbers: Gambling Betty and Jane are gambling. They are cutting cards (picking a random place in the deck to see a card). Whoever has the higher card wins the bet. If the cards have the same value (for example, they are both eights), they try again. Betty and Jane do this a 100 times. Tom and Bill are doing the same thing but are betting only 10 times. Is Bill or Betty more likely to end having very close to 50% wins? Explain. You may refer to the graph to help you decide. It is one simulation based on 100 trials.
Solution Summary: The author explains that Betty is more likely to end up having very close to 50% wins. The graph shows the percentage of wins for different number of trials.
Law of Large Numbers: Gambling Betty and Jane are gambling. They are cutting cards (picking a random place in the deck to see a card). Whoever has the higher card wins the bet. If the cards have the same value (for example, they are both eights), they try again. Betty and Jane do this a 100 times. Tom and Bill are doing the same thing but are betting only 10 times. Is Bill or Betty more likely to end having very close to 50% wins? Explain. You may refer to the graph to help you decide. It is one simulation based on 100 trials.
Morningstar tracks the total return for a large number of mutual funds. The following table shows the total return and the number of funds for four categories of mutual funds.
Click on the datafile logo to reference the data.
DATA file
Type of Fund
Domestic Equity
Number of Funds
Total Return (%)
9191
4.65
International Equity
2621
18.15
Hybrid
1419
2900
11.36
6.75
Specialty Stock
a. Using the number of funds as weights, compute the weighted average total return for these mutual funds. (to 2 decimals)
%
b. Is there any difficulty associated with using the "number of funds" as the weights in computing the weighted average total return in part (a)? Discuss. What else might be used for weights?
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c. Suppose you invested $10,000 in this group of mutual funds and diversified the investment by placing $2000 in Domestic Equity funds, $4000 in International Equity funds, $3000 in Specialty Stock…
The days to maturity for a sample of five money market funds are shown here. The dollar amounts invested in the funds are provided.
Days to
Maturity
20
Dollar Value
($ millions)
20
12
30
7
10
5
6
15
10
Use the weighted mean to determine the mean number of days to maturity for dollars invested in these five money market funds (to 1 decimal).
days
c. What are the first and third quartiles?
First Quartiles (to 1 decimals)
Third Quartiles (to 4 decimals)
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Which companies spend the most money on advertising? Business Insider maintains a list of the top-spending companies. In 2014, Procter & Gamble spent more than any other company, a whopping $5 billion. In second place was Comcast, which spent $3.08 billion (Business Insider website, December 2014). The top 12 companies and
the amount each spent on advertising in billions of dollars are as follows.
Click on the datafile logo to reference the data.
DATA file
Company
Procter & Gamble
Comcast
Advertising
($billions)
$5.00
3.08
2.91
Company
American Express
General Motors
Advertising
($billions)
$2.19
2.15
ETET
AT&T
Ford
Verizon
L'Oreal
2.56
2.44
2.34
Toyota
Fiat Chrysler
Walt Disney Company
J.P Morgan
a. What is the mean amount spent on advertising? (to 2 decimals)
2.55
b. What is the median amount spent on advertising? (to 3 decimals)
2.09
1.97
1.96
1.88
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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