Measurements were recorded for the slapshot speed of 100 minor-league hockey players. These measurements were found to be normally distributed with mean of 84.388 mph and standard deviation of 3.3706 mph. Would it be unusual to record a value above 94.6 mph?

Question 6 options:

According to estimates by the office of the Treasury Inspector General of IRS, approximately 0.0499 of the tax returns filed are fraudulent or will contain errors that are purposely made to cheat the IRS. In a random sample of 337 independent returns from this year, what is the probability that at least 26 will be fraudulent or will contain errors that are purposely made to cheat the IRS?

Question 7 options:

According to estimates by the office of the Treasury Inspector General of IRS, approximately 0.0362 of the tax returns filed are fraudulent or will contain errors that are purposely made to cheat the IRS. In a random sample of 385 independent returns from this year, what is the probability that less than 9 will be fraudulent or will contain errors that are purposely made to cheat the IRS?

Question 9 options:

2. Alice and 10 other users are sending packets using the pure ALOHA protocol. The duration of a packet is 40 msec. Each user sends a packet (including both originals and retransmissions) following a Poisson process with rate 1/400 packets/msec.

1. (a) What is the chance of success on Alice’ first attempt? (hint: the probability that there is no othertransmission within the vulnerable period of Alice’s attempt)

2. (b) What is the probability that Alice gets exactly k collisions and then a success? (hint: consider a Bernoulli trials process)

3. (c) What is the expected number of transmission attempts needed to successfully send a packet?

True or False:

13. A classical probability measure is a probability assessment that is based on relative frequency.

14. The probability of an event is the product of the probabilities of the sample space outcomes that correspond to the event.

15. If events A and B are independent, then P(A|B) is always equal to P(A).

16. Events that have no sample space outcomes in common and, therefore cannot occur simultaneously are referred to as mutually independent events.
17. The binomial experiment consists of n independent, identical trials, each of which results in either success or failure and the probability of success changes from trial to trial.
18. The standard deviation of a binomial distribution is np(1-p).

19. In a binomial distribution the random variable X is discrete.

20. The standard deviation and mean are the same for the standard normal distribution.

21. In a statistical study, the random variable X = 1, if the house is colonial and X = 0 if the house is not colonial, then it can be stated that the random variable is continuous.

22. For a continuous distribution, P(X ≤ 10) is the same as P(X<10).

23. For a continuous distribution, the exact probability of any particular value is always zero.

24. For a binomial probability experiment, with n = 60 and p =.2, it is appropriate to use the normal approximation to the binomial distribution without continuity correction.

25. All continuous random variables are normally distributed.

5. (Casella & Berger, 2nd ed.) A p.d.f. is defined by f(x, y) = C(x + 2y) for 0 < y < 1 and 0 < x < 2, and is zero otherwise. a) Find the value of C. b) Are X and Y independent? c) Find the marginal p.d.f of X. d. Find the conditional p.d.f fy|x(y|x). e) Find E[Y |x = 1].

(1) According to the American Lung Association, 90% of adult smokers started smoking before turning
21 years old. Ten smokers 21 years old or older were randomly selected, and the number of smokers
who started smoking before 21 is recorded.
(a) State the distribution of the random variable of number of smoker of these 10 who started
smoking before age 21 and its two parameters.
(b) Find the probability that exactly 8 of them started smoking before 21 years of age. Do not
use statistical features of your calculator.
(c) Find the probability that fewer than 8 of them started smoking before 21 years of age.
(d) Find the probability that between 7 and 9 of them, inclusively, started smoking before 21 years
of age.
(e) Compute and interpret the mean of this random variable.
(f) Compute the standard deviation of this random variable.

Your patient’s mammogram is positive for breast cancer which has a fairly low rate in your state of 1 case per 1,000 women annually. You know from the literature that the mammogram test has a sensitivity of around 92% and a specificity of 95% depending on the study. What do you tell your patient when she asks do I have breast cancer.

Show your work in both a contingency table and using the shortcut Bayes Theorem.

For staffing purposes, a retail store manager would like to standardize the number of checkout lanes to keep open on a particular shift. She believes that if the standard deviation of the hourly customer arrival rates is 9 customers or less, then a fixed number of checkout lanes can be staffed without excessive customer waiting time or excessive clerk idle time. However, before determining how many checkout lanes (and thus clerks) to use, she must verify that the standard deviation of the arrival rates does not exceed 9. Accordingly, a sample of 25 hourly customer arrival rates was compiled for that shift over the past week.

a. Select the hypotheses to test whether the standard deviation of the customer arrival rates exceeds 9.

• H₀: σ² ≤ 81; H_A: σ² > 81

• H₀: σ² = 81; H_A: σ² ≠ 81

• H₀: σ² ≥ 81; H_A: σ² < 81

b. Calculate the value of the test statistic. Assume that customer arrival rates are normally distributed. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Test Statistic: ???

Your leader wants you to evaluate the difference in cycle time between three different offices. Describe the steps you would take in the evaluation in order to provide a report so the leader can take action. In replies to peers, indicate whether you agree or disagree with the steps they outlined. Justify your response using what you learned from the topic materials

Because some people are unable to stand to have their height measured, doctors use the height from the floor to the knee to approximate their patients’ height (in cm).

a. Use Excel to determine the correlation coefficient of this data

b. Use Excel to determine the regression equation of this data

c. Find the overall height from a knee height of 45.3 cm

d. Find the overall height from a knee height of 52.7 cm

Choose one • 20 points

• a. r = 0.73220213

  b. Equation: y = 2.0217x + 67.746

  c. 159.32901

  d. 174.28959

• a. r = 0.82544241

  b. Equation: y = 2.5109x + 40.79

  c. 154.53377

  d. 173.11443

• a. r = 0.53611996

  b. Equation: y = 2.0217x + 67.746

  c. 159.32901

  d. 174.28959

• a. r = 0.908553861

  b. Equation: y = 2.5109x + 40.79

  c. 154.53377

  d. 173.11443

A large pond contains f fish, of which t have been tagged. Biologist A takes a simple random sample of nA fish from the pond. Biologist B takes a simple random sample of nB fish from the fish that remain in the pond after Biologist A has drawn her sample. You can assume that nA+nB<t.

a) Fill in the blank with a math expression involving any or all of f, t, nA, and nB. Explain your answer.

The number of tagged fish in Biologist A's sample has expectation _____________.

b) Fill in the blank (carefully!) with a math expression involving any or all of f, t, nA, and nB. Explain your answer.

The number of tagged fish in Biologist B's sample has expectation __________.

c) Fill in the blank with a math expression involving any or all of f, t, nA, and nB. Explain your answer.

The number of tagged fish that don't get into the samples has expectation_________.

A standardized test consists of 100 multiple-choice questions. Each question has five possible answers, only one of which is correct. Four points are awarded for each correct answer. To discourage guessing, one point is taken away for every answer that is not correct (this includes answers that are missing).

The company that creates the test has to understand how well a student could do just by random guessing. Suppose a student answers each question by picking one of the five choices at random independently of the choices on all other questions. Let S be the student's score on the test.

a) Find ?(S).

b) Find P(S>10). Write your answer as a math expression, then use the code cell below to find its numerical value and provide it along with your math expression.

1. A researcher is interested to learn if there is a linear relationship between the hours in a week spent exercising and a person’s life satisfaction. The researchers collected the following data from a random sample, which included the number of hours spent exercising in a week and a ranking of life satisfaction from 1 to 10 ( 1 being the lowest and 10 the highest). PLEASE help in SPSS.

1. Find the mean hours of exercise per week by the participants.
2. Find the variance and standard deviation of the hours of exercise per week by the participants.
3. Run a bivariate correlation to determine if there is a linear relationship between the hours of exercise per week and the life satisfaction. Report the results of the test statistic using correct APA formatting.
4. Run a linear regression on the data. Report the results, using correct APA formatting. Identify the amount of variation in the life satisfaction ranking that is due to the relationship between the hours of exercise per week and the life satisfaction (Hint: the R² value)
5. Report a model of the linear relationship between the two variables using the regression line formula.

Case Study: Project Communications Management: Best Practices in Practice As part of a large IT systems integration project for the State of California, I witnessed the Project Management Office (PMO) do an excellent job of ensuring that the project stakeholders were properly informed of the project’s progress, outstanding issues, risks, and change requests. Information was gathered from multiple sources (for example, Project Schedule, Issue and Risk Repositories, Testing Tool Data Metrics, Change Request Log, and so on) and compiled into a comprehensive weekly status report that was shared with the stakeholders. In addition, detailed risk and issue status reports were prepared and shared in the weekly risk and issue management meetings. Also, the overall project performance status was communicated to the control agencies (for example, California Department of Technology, Department of Finance, and so on) via a monthly Project Status Report (aka PSR) containing a variety of performance tracking metrics. All questions were responded to, and all ambiguities were clarified in a timely manner to ensure that the information was clearly understood by the recipients as intended and everyone was on the same page. The project director was a strong proponent of information quality who took a keen interest in monitoring the quality of the content and delivery of the status reports and suggested improvements when necessary. Case Study Questions 1. What project communications best practices did the project practice? 2. How was the project performance status communicated to the control agencies? 3. What role did the project director play in enhancing the project communications management? 4. What are the lessons learned from this case?

Components of a certain type are shipped to a supplier in batches of ten. Suppose that 49% of all such batches contain no defective components, 31% contain one defective component, and 20% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0, 1, and 2 defective components being in the batch under each of the following conditions? (Round your answers to four decimal places.)

(a) Neither tested component is defective.

(b) One of the two tested components is defective. [Hint: Draw a tree diagram with three first-generation branches for the three different types of batches.]

Evaluate the differences between dependent and independent samples. Provide an example of each type of sample.