True or False.
(a) According to the Heisenberg Uncertainty Principle, it is impossible to know simultaneously both the exact
momentum of the electron and its exact location in space.
Answer: ____________
(b) According to Born, taking the square root of ψ would give the probability of finding the electron in a certain
region of space at a given time.
Answer: ____________
(c) Based on the results from blackbody radiation, Max Planck assumed that energy can only be emitted in
discrete amounts.
Answer: ____________
(d) Niels Bohr postulated that when an electron changes from the higher energy state to the lower energy state,
electromagnetic radiation is released.
Answer: ____________
(e) Electromagnetic radiations with different wavelengths have different effect on matter.
Answer: ____________
(f) In line spectra, photons are emitted at discrete wavelengths.
Answer: ____________
(g) The principle quantum number describes the energy of the orbital.
Answer: ____________
(h) Valence electrons are the core electrons used for forming chemical bonds.
Answer: ____________
(i) The angular momentum quantum number describes the shape of the orbital.
Answer: ____________
(j) All s orbital are spherical with the same size.
Answer: ____________

Consider a pharmaceutical company that produces flu vaccines that are good with reliability p = 0.9, independently from vaccine to vaccine. Assume that you three vaccines to test whether they are effective or not. Define the random variable X as the number of effective vaccines circuits that you obtain after testing each of the three selected ones. Define the random variable Y as the number of vaccines that you test from the three before you find an ineffective one. If all three vaccines are found to be effective, let Y = 3. Note both X, Y can take the value 0. (a) Find the possible values of X, Y . (b) Compute the joint PMF of X, Y as a matrix. (c) Compute the for the marginal probability mass function (PMF) of X. (d) Compute the marginal PMF PY (y) of the random variable Y . (e) Compute the conditional pmf PY |X(y|x) for all possible values of x, y. (f) Compute E[Y |X = 1] (g) Compute the expected values E[X], E[Y ].

1. Categorize these measurements associated with student life according to level: nominal, ordinal, interval, or ratio.

1 (a) Length of time to complete a test

a)nominal

b)ordinal     

c)interval

d) ratio

1(b) Time of first class

a) nominal

b) ordinal     

c) interval

d) ratio

1(c) Major field of study

a) nominal

b) ordinal    

c) interval

d) ratio

1(d) Course evaluation scale: poor, acceptable, good

a) nominal

b) ordinal    

c) interval

d) ratio

1(e) Score on last test (based on 100 possible points)

a) nominal

b) ordinal    

c) interval

d) ratio

1(f) Age of student

a) nominal

b) ordinal    

c) interval

d)ratio

2. Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)

μ = 20; σ = 4.2

P(x ≥ 30) = ______

3. Compute P_5,4. (Enter an exact number.) =______

Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows.

(a)

Consider a random sample of size n = 2 (two customers), and let

X

be the sample mean number of packages shipped. Obtain the probability distribution of

X.

(b)

Refer to part (a) and calculate

P(X ≤ 2.5).

(c)

Again consider a random sample of size n = 2, but now focus on the statistic R = the sample range (difference between the largest and smallest values in the sample). Obtain the distribution of R. [Hint: Calculate the value of R for each outcome and use the probabilities from part (a).]

(d)

If a random sample of size n = 4 is selected, what is

P(X ≤ 1.5)?

[Hint: You should not have to list all possible outcomes, only those for which

x ≤ 1.5.]

Valles Global Industries (VGI) is getting ready to market their Internet-based party planning service. One of the menu items is a kabob. The kabob was designed to have four vegetable chunks and three chunks of protein: beef, chicken, shrimp or tofu. On average, any vegetable will yield 5 chunks suitable for a kabob. One of any ten vegetables will be of poor quality and cannot be used. In presenting a menu and budget to a party-thrower, VGI recommends two kabobs per person.

1. VGI also offers a statistical modeling program that prevents food waste. They have data that recommends a mean number of party attenders as well as metrics on variability. Imagine you are planning an event with VGI. They suggest the number of party-attenders for a 200 person party estimate is actually distributed N(150, 1225). They also recommend using a probability of 90 percent for attendees. If VGI charges you $100 per attendee, how much does their recommendation save you?
2. Referring to A above, would you take their recommendation? Why or why not?

Employment Discrimination Practice Sheet

Instructions:

1. Match the employment law term with the correct employment situation. Use each term only once. Also, answer the question in the situation.

Employment Law Terms

1. Age Discrimination in Employment Act of 1967
2. Americans with Disabilities Act of 1990
3. Bona fide occupational qualification
4. Disparate impact
5. Disparate treatment
6. Employment at-will
7. Equal Pay Act of 1963
8. Retaliation
9. Sexual harassment: Hostile Work Environment
10. Sexual harassment: Quid Pro Quo

6. ______________________________ The Duke Power Company adopted a requirement that applicants for hire or transfer to any department but the labor department had to have a high school diploma or receive a satisfactory score on two IQ tests. As a result of these requirements, African American employees were denied jobs and promotions. (Griggs v. Duke Power Co., 401 U.S. 424 (1971)) Are these requirements discriminatory if they are not related to job performance? If so, under what theory could an employee or applicant file a complaint?

7. ______________________________ Your employer states that upon turning 65, all traveling sales employees must turn over their territories to younger workers and begin handling in-office file work only. If you can show that at age 65 or above you are just as capable and competitive out on the road as your younger counterparts, can you bring a claim stating that this practice will adversely impact your income or other benefits? If so, under what law?

8. ______________________________ Malia, a hard worker who is praised by her coworkers and clients alike, is looking forward to receiving her first annual bonus after working for the company for more than three years. When she does not receive the bonus and finds out that a co-worker, who has only been at the company for four months, does, Malia is upset. When she questions her supervisor, she is told that she could not be given the bonus because she did not have a college degree. She then discovers that the newly-promoted Walter does not have a degree either. Does Malia have a discrimination claim? If so, under what law?

9. ______________________________ A trucking company conducts job interviews in a second floor office where there is no elevator. The company calls Tanya to arrange for an interview for a secretarial position. She requests a reasonable accommodation because she uses a wheelchair. Installing an elevator would be an undue hardship, so what could the company do to provide a reasonable accommodation? What law is relevant here?

10. ______________________________ Samuel was uncomfortable with the sexual jokes his co-workers regularly posted in the break room. He told his manager who did not address the issue. He then went to Human Resources to see what options he had in this situation. When his manager heard that Samuel when to HR, his manager told Samuel to suck it up and took away the extra overtime shift Samuel had been working. The manager’s actions are an example of what?

A student can enter a course either as a beginner (73%) or as a transferring student (27%). It is found that 62% of beginners eventually graduate, and that 78% of transfers eventually graduate. Find:

1. the probability that a randomly chosen student is a beginner who will eventually graduate,

2. the probability that a randomly chosen student will eventually graduate,

3. the probability that a randomly chosen student is either a beginner or will eventually graduate, or both.

4. Are the events ‘eventually graduate’ and ‘enters as a transferring student’ statistically independent?

5. If a student eventually graduates, what is the probability that the student entered as a transferring student?

6. If two entering students are chosen as random, what is the probability that not only do they enter in the same way but that they also both graduate or fail?

A source transmitted a message through a noisy channel. Each symbol is 0 or 1 with probability p and 1 − p, respectively and is received incorrectly with probability 0 and 1. Errors in different symbol transmission are independent.

(a) What is the probability that the kth symbol is received correctly?

(b) What is the probability that the string of symbols 0111 is received correctly?

(c) To improve reliability, each symbol is transmitted three times and the received string is decoded by majority rule. For example, a 0 is transmitted as 000 and is decoded at the receiver as a 0 if and only if the received three symbol string contains at least two 0s. Similar rule applies to 1. What is the probability that a 0 is corrected decoded?

Show me how it is done in Excel if possible:

A store has one counter. The probability of inter-arrival time (in min) and service time (in min.) of customers are given in the following table.

Distribution of time between Arrival

Distribution of Service-Time