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Sixty ounces of a 50% gold alloy are mixed with 40 oz of a 40% gold alloy. Find the percent concentration of the resulting gold alloy.
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In A Previous Lab We Tested The Following Hypotheses
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Math 161A Statistics Probability Writing Project
1. (6 points) How large would a potential Jackpot have to be in the California Mega
Millions Lottery in order for the gam ...
Math 161A Statistics Probability Writing Project
1. (6 points) How large would a potential Jackpot have to be in the California Mega
Millions Lottery in order for the game to be fair? Present your computation and
explain your reasoning in addition to stating your final answer.
Note: A fair game is one in which in the long-run neither party (lottery company
and players) has an advantage.
2. There are a number of probability claims made in the Lottery tips. In this problem,
you will verify whether these claims are true. Consider the current rules (5/70 +
1/25) of the CA MEGA millions game.
(a) (5 points) Consider the Odd-Even Lotto Tip. Find the exact probability that
the five white numbers selected will all be even.
(b) (8 points) Consider the Sum Lotto Tip. Use the Central Limit Theorem to
approximate the probability that the sum of the five white balls will fall between
132 and 223 (both inclusive).
Discuss the appropriateness of using the Central Limit Theorem in this case. If
any of the assumptions of the theorem are violated, state what these assumtions
are and discuss how extreme (mild, moderate, severe) the violation is.
(c) (6 points) Consider the Repeat Hits Lottery Tip. It is not entirely clear, whether
this tip only concerns the white balls or also the gold MEGA ball.
i. Find the exact probability that in a given drawing at least one of the white
numbers is a repeat from the last drawing.
ii. Find the exact probability that in a given drawing at least one of the six
balls drawn (five white and one gold) is a repeat of the last drawing.
(d) (5 points) Consider the Tip that recommends to avoid previous number combinations. How long, on average (in years), will it take until a given set of MEGA
million lottery numbers (five white balls and MEGA ball) will be repeated in
a drawing? Recall, that drawings take place bi-weekly and that assume that a
year has 365 days (i.e., ignore leap years).
3. (5 points) Assume that game payouts are fixed (not pari-mutuel). Will following the
advice of the lottery expert increase your chances of winning the lottery? (This is a
multiple choice question - Yes/No answer ONLY.)
4. (10 points) Discuss the advice from the Lotto-Expert presented on page 2. Are the
statements made in the individual tips presented there generally truthful? Do they
hold for general (future) drawings, and not just for data collected in the past? Is
following this advice a good idea when playing the lottery? Explain why or why not.
Take a stand and defend your position with a good logical argument using the
methods of probability you have learned in this course. Provide as much numerical
evidence as necessary (you may cite your results from problem 2) to support your
3
Math 161A - Fall 2020 M. Bremer
claim(s). Make sure to provide a cohesive argument (using correct spelling and good
grammar).
5. (5 points) To study whether the drawing of lottery numbers for the MEGA million
game is truly random, we will consider some data. The data (which are available
in the file “Lottery Data.csv”) contains the date of the drawing, the five white balls
drawn, and the MEGA ball drawn in all 1925 drawings of the NY MEGA millions
between 5/17/2002 and 11/03/2020.
Based on the graphs that you can find on the next pages, discuss whether it is reasonable to assume that lottery numbers are drawn independently and at random
meaning that each possible number combination is equally likely to be drawn. Describe which aspect(s) of which graph(s) you base your conclusion on.
Disclaimer: The data come from the New York State (not the California State)
MEGA millions lottery. Like California, NY has changed the rules for the MEGA
millions game several times over the last couple years. For instance, on October 19,
2013, they switched from drawing 55 white balls to drawing 75 white balls. On the
same date, the number of possible MEGA balls were reduced from 45 to 15. Another
rule change occurred in October 2017.
Note: You are welcome to look at the raw data and/or create your own additional
graphs if you wish, but that’s not required for this problem.
Grading: Your work will be graded
6 pages
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Most Popular Content
investment opportunities
An investor not wanting to miss out on possible investment opportunities considers investing $20,000 in the stock market. ...
investment opportunities
An investor not wanting to miss out on possible investment opportunities considers investing $20,000 in the stock market. He believes that the probability is 0.30 that the market will improve, 0.37 that it will stay the same, and 0.33 that it will deteriorate. Further, if the economy improves, he expects his investment to grow to $28,000, but it can also go down to $17,000 if the economy deteriorates. If the economy stays the same, his investment will stay at $20,000.a. what is the expected value of his investmentb. What should the investor do if he is risk neutral...take it or not take itc. s the decision clear-cut if he is risk averse
3 pages
In A Previous Lab We Tested The Following Hypotheses
1. In a previous lab we tested the following hypotheses, μ is the mean number of alcoholic drinks consumed by In a random ...
In A Previous Lab We Tested The Following Hypotheses
1. In a previous lab we tested the following hypotheses, μ is the mean number of alcoholic drinks consumed by In a random sample of 75 students, the ...
Math 161A Statistics Probability Writing Project
1. (6 points) How large would a potential Jackpot have to be in the California Mega
Millions Lottery in order for the gam ...
Math 161A Statistics Probability Writing Project
1. (6 points) How large would a potential Jackpot have to be in the California Mega
Millions Lottery in order for the game to be fair? Present your computation and
explain your reasoning in addition to stating your final answer.
Note: A fair game is one in which in the long-run neither party (lottery company
and players) has an advantage.
2. There are a number of probability claims made in the Lottery tips. In this problem,
you will verify whether these claims are true. Consider the current rules (5/70 +
1/25) of the CA MEGA millions game.
(a) (5 points) Consider the Odd-Even Lotto Tip. Find the exact probability that
the five white numbers selected will all be even.
(b) (8 points) Consider the Sum Lotto Tip. Use the Central Limit Theorem to
approximate the probability that the sum of the five white balls will fall between
132 and 223 (both inclusive).
Discuss the appropriateness of using the Central Limit Theorem in this case. If
any of the assumptions of the theorem are violated, state what these assumtions
are and discuss how extreme (mild, moderate, severe) the violation is.
(c) (6 points) Consider the Repeat Hits Lottery Tip. It is not entirely clear, whether
this tip only concerns the white balls or also the gold MEGA ball.
i. Find the exact probability that in a given drawing at least one of the white
numbers is a repeat from the last drawing.
ii. Find the exact probability that in a given drawing at least one of the six
balls drawn (five white and one gold) is a repeat of the last drawing.
(d) (5 points) Consider the Tip that recommends to avoid previous number combinations. How long, on average (in years), will it take until a given set of MEGA
million lottery numbers (five white balls and MEGA ball) will be repeated in
a drawing? Recall, that drawings take place bi-weekly and that assume that a
year has 365 days (i.e., ignore leap years).
3. (5 points) Assume that game payouts are fixed (not pari-mutuel). Will following the
advice of the lottery expert increase your chances of winning the lottery? (This is a
multiple choice question - Yes/No answer ONLY.)
4. (10 points) Discuss the advice from the Lotto-Expert presented on page 2. Are the
statements made in the individual tips presented there generally truthful? Do they
hold for general (future) drawings, and not just for data collected in the past? Is
following this advice a good idea when playing the lottery? Explain why or why not.
Take a stand and defend your position with a good logical argument using the
methods of probability you have learned in this course. Provide as much numerical
evidence as necessary (you may cite your results from problem 2) to support your
3
Math 161A - Fall 2020 M. Bremer
claim(s). Make sure to provide a cohesive argument (using correct spelling and good
grammar).
5. (5 points) To study whether the drawing of lottery numbers for the MEGA million
game is truly random, we will consider some data. The data (which are available
in the file “Lottery Data.csv”) contains the date of the drawing, the five white balls
drawn, and the MEGA ball drawn in all 1925 drawings of the NY MEGA millions
between 5/17/2002 and 11/03/2020.
Based on the graphs that you can find on the next pages, discuss whether it is reasonable to assume that lottery numbers are drawn independently and at random
meaning that each possible number combination is equally likely to be drawn. Describe which aspect(s) of which graph(s) you base your conclusion on.
Disclaimer: The data come from the New York State (not the California State)
MEGA millions lottery. Like California, NY has changed the rules for the MEGA
millions game several times over the last couple years. For instance, on October 19,
2013, they switched from drawing 55 white balls to drawing 75 white balls. On the
same date, the number of possible MEGA balls were reduced from 45 to 15. Another
rule change occurred in October 2017.
Note: You are welcome to look at the raw data and/or create your own additional
graphs if you wish, but that’s not required for this problem.
Grading: Your work will be graded
6 pages
20200813212450math265 Course Project Part B 2 1
In this part of the project, you will model the behavior of a resistor-inductor (RL) circuit in a transient Initially, the ...
20200813212450math265 Course Project Part B 2 1
In this part of the project, you will model the behavior of a resistor-inductor (RL) circuit in a transient Initially, the DC voltage source is off ...
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