Probability - punditwritersbay.com

A number is chosen from the set of numbers S = {11, 12, 13, 14, 15, 16, 17, 18,

A number is chosen from the set of numbers S = {11, 12, 13, 14, 15, 16, 17, 18, 19}. Find the probability
1. the number is even
2.the number is a prime number.
3.the number is odd and less than 17

1. How are permutations different from combinations? 2. Suppose there are 365

1. How are permutations different from combinations?
2. Suppose there are 365

1. How are permutations different from combinations?
2. Suppose there are 365 days in a year and we are ignoring leap years. Suppose there are n property owners’ club of which you are not a member. You can only become a member if the registration date of your property matches with that of any of the n owners.
a. What is the probability of this match (in terms of n)? Hint: find the probability of the complement event.
b. What should n be for chances of the match being 50%? Why may this number be different from 365/2?
c. Suppose they refuse you a membership in the club. For you to challenge them, you need to show that none of the n existing owners have their registration on the same day. What is the probability of this happening? You may leave the answer as an expression, instead of a number.
3. An insurance company finds that Mark has a 8% chance of getting into a car accident in the next year. If Mark has any kind of accident then the company guarantees to pay him $10, 000. The company has decided to charge Mark a $200 premium for this one year insurance policy.
a. Let X be the amount of profit or loss from this insurance policy in the next year for the insurance company. Find EX, the expected return for the Insurance company? Should the insurance company charge more or less on its premium?
b. What amount should the insurance company charge Mark in order to guarantee an expected return of $100? [10%]
4. Suppose that, some time in the distant future, the average number of burglaries in New York City in a week is 2.2. Approximate the probability that there will be
a. no burglaries in the next week;
b. at least 2 burglaries in the next week.
5. A NYU student claims that she can distinguish Van Leewen ice cream from Hagen Dazs’s ice cream. There are 60% chance of her claim to be true.
a. What is the probability that she needs to test 8 samples to guess the ice cream correctly for the first time. How many ice creams does she need to test on average to arrive at the first correct guess?
b. What is the probability her 8th correct guess comes with the 10th sample that she tastes?

A bag contains 5 red marbles, 8 blue marbles, and 7 green marbles. If a marble i

A bag contains 5 red marbles, 8 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is either red or green?
To solve this, you can use the formula for the probability of an event ( P(E) ):
P(E)=Number of favorable outcomesTotal number of possible outcomesP(E)=Total number of possible outcomes

Continue working on your project. You will now test your hypotheses using boots

Continue working on your project. You will now test your hypotheses using bootstrapping. You should preform two bootstraps one on the categorical and the quantitative. Be sure to include and edits suggested in your instructor’s review or the peer review. Due Monday at Noon.
Please use the data you originally collected for part 1. You will add these new parts to report part 2, 3, and 4.
1. For this project, you must nd some published or existing data. Possible sources include: almanacs, magazines and journal articles, textbooks, web resources, athletic teams, newspapers, professors with experimental data, campus organizations, electronic data repositories, etc. Your dataset must have at least 25 cases, two categorical variables and two quantitative variables. It is also recommended that you are interested in the material included in the dataset.
2. Use bootstrapping to do the analysis.
(a) Compute the standard error for the quantitative variable that you set up the hypothesis test for in part 4 using bootstrapping. Report a 95% confidence interval and decide if you are able to reject or fail to reject your null hypothesis. Create a histogram for your bootstrap distribution.
(b) Compute the standard error for the categorical variable that you set up the hypothesis test for in part 4 using bootstrapping. Report a 95% confidence interval and decide if you are able to reject or fail to reject your null hypothesis. Create a histogram for your bootstrap distribution.2. Use the techniques of the text to repeat your hypothesis test.
3.Use bootstrapping to do the analysis.
(a) Repeat your hypothesis test on the categorical variable utilizing the appropriate formulas for your situation. Compute 95% con dence interval and compare to results from bootstrapping.
4. Add to your report!
(a) Include all items requested above. Include text and graphics describing the processes you have completed.

Your task: submit a single PDF document with the answers to the following proble

Your task: submit a single PDF document with the answers to the following problems.
1. Complete the following (method to implement empirical data in a tree):
a. Determine the 0.05, 0.10, 0.25, 0.50, 0.75, 0.90, 0.95 quantiles for the high temperature recorded on March 17. . The data for years between 1995 and 2014 is shown below.
b. Plot your assessed quantiles as a CDF.
c. Construct a three-point approximation to the distribution using the extended Pearson-Tukey method. Show the three temperatures, fractiles, and probabiltities in a table.
d. Construct an approximation using the extended Swanson-Megill method. Show the three temperatures, fractiles, and probabiltities in a table.
2. Complete the following (method to implement a continuous distribution in a tree):
a. Suppose you know the expected life of an engine is exponentially distributed with a mean life of 1000 hours.
b. Construct a three-point approximation to the distribution using the extended Pearson-Tukey method. Show the three Engine Hours, fractiles, and probabiltities in a table.
c. Construct a three-point approximation to the distribution using the extended Swanson-Megill method. Show the three Engine Hours, fractiles, and probabiltities in a table.
High temperature on St. Patrick’s Day in Chicago
201441
201338
201273
201170
201062
200970
200843
200738
200642
200555
200435
200371
200242
200135
200037
199971
199846
199751
199654
199563

Your task: submit a single PDF document with the answers to the following proble

Continue working on your project. You will now analyze one quantitative variable

Continue working on your project. You will now analyze one quantitative variable and generate two graphics. Be sure to include and edits suggested in your instructor’s review or the peer review. Due Monday at Noon.
Please use the data you originally collected for part 1. You will add these new parts to report part 2.
1. For this project, you must find some published or existing data. Possible sources include: almanacs, magazines and journal articles, textbooks, web resources, athletic teams, newspapers, professors with experimental data, campus organizations, electronic data repositories, etc. Your dataset must have at least 25 cases, two categorical variables and two quantitative variables. It is also recommended that you are interested in the material included in the dataset.
2. Utilizing technology, analyze your dataset.
(a) For at least one of the quantitative variables, include summary statistics (mean, standard deviation, ve number summary) and two graphical displays (histogram and box plot). Are there any outliers? Is the distribution symmetric, skewed, or some other shape?
4. For this project you must find some published or existing data. Possible sources include: almanacs,magazines and journal articles, textbooks, web resources, athletic teams, newspapers, professors with experimental data, campus organizations, electronic data repositories, etc. Your dataset must have at least 25 cases, two categorical variables and two quantitative variables. It is also recommended that you are interested in the material included in the dataset.
5. Decide what to analyze.
(a) Set up a hypothesis test for a quantitative variable. You may compare to a suspected parameter or compare two computed statistics. State your null and alternative hypothesis in the correct formatting:
H0: parameter = value
Ha: parameter ≠ value
(b) Set up a hypothesis test for a categorical variable. You may compare to a suspected parameter or compare two computed proportions. State your null and alternative hypothesis in the correct formatting:
H0: p = value
Ha: p ≠ value
6. Add to your report!
(a) Include all items requested above. Include text about each and why these hypothesis decisions were made