Exercises for Probability

Exercise 2-17

Evertight, a leading manufacturer of quality nails, produces 1-, 2-, 3-, 4-, and 5-inch nails for various uses. In the production process, if there is an over- run or the nails are slightly defective, they are placed in a common bin. Yesterday, 651 of the 1-inch nails, 243 of the 2-inch nails, 41 of the 3-inch nails, 451 of the 4-inch nails, and 333 of the 5-inch nails were placed in the bin.

1. What is the probability of reaching into the bin and getting a 4-inch nail?
2. What is the probability of getting a 5-inch nail?
3. If a particular application requires a nail that is 3 inches or shorter, what is the probability of getting a nail that will satisfy the requirements of the application?

Exercise 2-18

Last year, at Northern Manufacturing Company, 200 people had colds during the year. One hundred fifty- five people who did no exercising had colds, and the remainder of the people with colds were involved in a weekly exercise program.  Half of the 1,000 employees were involved in some type of exercise.

1. What is the probability that an employee will have a cold next year?
2. Given that an employee is involved in an exercise program, what is the probability that he or she will get a cold next year?
3. What is the probability that an employee who is not involved in an exercise program will get a cold next year?
4. Are exercising and getting a cold independent events? Explain your answer.

Exercise 2-27

In a sample of 1,000 representing a survey from the entire population, 650 people were from Laketown, and the rest of the people were from River City. Out of the sample, 19 people had some form of cancer.  Thirteen of these people were from Laketown.

1. Are the events of living in Laketown and having some sort of cancer independent?
2. Which city would you prefer to live in, assuming that your main objective was to avoid having cancer?

Exercise 1

An engineering company advertises a job in three papers, A, B and C. It is known that these papers attract undergraduate engineering readerships in the proportions 2:3:1. The probabilities that an engineering undergraduate sees and replies to the job advertisement in these papers are 0.002, 0.001 and 0.005 respectively. Assume that the undergraduate sees only one job advertisement.

1. If the engineering company receives only one reply to it advertisements, calculate the probability that the applicant has seen the job advertised in place A.
2. If the company receives two replies, what is the probability that both applicants saw the job advertised in paper A?

Exercise 2-33

Gary Schwartz is the top salesman for his company.  Records indicate that he makes a sale on 70% of his sales calls. If he calls on four potential clients, what is the probability that he makes exactly 3 sales? What is the probability that he makes exactly 4 sales?

Exercise 2

A special five football matches series will be played between UAE and KSA. The probability that UAE will win a match against KSA is 0.6.              

            (i). What is the probability that UAE will win at least 3 matches in the series?        

            (ii). What is the probability that UAE will lose all the matches of the series?          

            (iii). What is the probability that UAE will win at most 2 matches in the series?     

Exercise 2-34

Trowbridge Manufacturing produces cases for personal computers and other electronic equipment. The quality control inspector for this company believes that a particular process is out of control. Normally, only 5% of all cases are deemed defective due to   discolorations. If 6 such cases are sampled, what is the probability that there will be 0 defective cases if the process is operating correctly? What is the probability that there will be exactly 1 defective case?

Exercise 2-34

If 10% of all disk drives produced on an assembly line are defective, what is the probability that there will be exactly one defect in a random sample of 5 of these? What is the probability that there will be no defects in a random sample of 5?

Exercise 2-38

Steve Goodman, production foreman for the Florida Gold Fruit Company, estimates that the average sale of oranges is 4,700 and the standard deviation is 500 oranges. Sales follow a normal distribution.

(a)  What is the probability that sales will be greater than 5,500 oranges?

(b)  What is the probability that sales will be greater than 4,500 oranges?

(c)  What is the probability that sales will be less than 4,900 oranges?

(d) What is the probability that sales will be less than 4,300 oranges?

Exercise 2-41

The time to complete a construction project is normally distributed with a mean of 60 weeks and a standard deviation of 4 weeks.

(a)  What is the probability the project will be finished in 62 weeks or less?

(b) What is the probability the project will be finished in 66 weeks or less?

(c)  What is the probability the project will take longer than 65 weeks?

Exercise 2-42

A new integrated computer system is to be installed worldwide for a major corporation.  Bids on this project are being solicited, and the contract will be awarded to one of the bidders. As a part of the proposal for this project, bidders must specify how long the project will take. There will be a significant penalty for finishing late. One potential contractor determines that the average time to complete a project of this type is 40 weeks with a standard deviation of 5 weeks. The time required to complete this project is assumed to be normally distributed.

1. If the due date of this project is set at 40 weeks, what is the probability that the contractor will have to pay a penalty (i.e., the project will not be finished on schedule)?
2. If the due date of this project is set at 43 weeks what is the probability that the contractor will have to pay a penalty (i.e., the project will not be finished on schedule)?
3. If the bidder wishes to set the due date in the proposal so that there is only a 5% chance of being late (and consequently only a 5% chance of having to pay a penalty), what due date should be set?

Exercise 2-43

Patients arrive at the emergency room of Costa   Valley Hospital at an average of 5 per day. The demand for emergency room treatment at Costa Valley follows a Poisson distribution.

(a)  Using Appendix C, compute the probability of exactly 0, 1, 2, 3, 4, and 5 arrivals per day.

(b)  What is the sum of these probabilities, and why is the number less than 1?

Exercise 2-44

Using the data in Problem 2-43, determine the probability of more than 3 visits for emergency room service on any given day.

A uranium and iron atom reside a distance R = 58.70 nm apart. The uranium atom is singly ionized; the iron atom is doubly ionized. Calculate the distance r from the uranium atom necessary for an electron to reside in equilibrium. Ignore the insignificant gravitational attraction between the particles.

What is the magnitude of the force on the electron from the uranium ion?

In winter a lake has a 0.30m thick ice layer over 1.20m of water. A light beam from above strikes a spot on the ice, making a 29? angle with the normal.

Part A

How far horizontally from that spot does the light ray strike the lake bottom?

Would it be useful to have an encryption that is additive and multiplicative in Homomorphic?

A small solid sphere of mass M₀, of radius R₀, and of uniform density ρ₀ is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls, U-Unchanged), when that sphere is replaced by a new solid sphere of uniform density.

The new sphere has radius R > R₀ and density ρ < ρ₀

The new sphere has radius R = R₀ and mass M < M₀

The new sphere has mass M < M₀ and density ρ = ρ₀

The new sphere has density ρ = ρ₀ and mass M > M₀

The new sphere has mass M = M₀ and density ρ > ρ₀

The new sphere has mass M = M₀ and density ρ < ρ₀

Blood type AB is found in only 3% of the population.† If 330 people are chosen at random, find the probability of the following. (Use the normal approximation. Round your answers to four decimal places.)

(a) 5 or more will have this blood type


(b) between 5 and 10 will have this blood type

The following information is to be used for the next two questions. Molar absorptivity data for the cobalt and nickel complexes with 2,3-quinoxalinedithiol are ε_Co = 36400 and ε_Ni = 5520 at 510 nm and ε_Co = 1240 and ε _Ni = 17500 at 656 nm. A 0.514-g sample was dissolved and diluted to 100.0 mL. A 25.0-mL aliquot was treated to eliminate interferences; after addition of 2,3-quinoxalinedithiol, the volume was adjusted to 50.0 mL. This solution had an absorbance of 1.246 at 510 nm and 0.367 at 656 nm in a 1.00-cm cell.

1. Calculate the concentration of cobalt (in ppm) in the initial solution prepared by dissolving the sample.

2. Calculate the concentration of nickel (in ppm) in the initial solution prepared by dissolving the sample.

ECO 345 – BOP Assignment Determine how each of the following transactions are entered into the US balance of payments?

1. Boeing Corporation sells five passenger planes to China for $35,000,000 China pays $5,000,000 of this amount in cash out her dollar deposits with Citibank in New York. The remainder of the amount is financed by the Export-Import Bank of the United States.

We will use El Paso information for our python script to compute property taxes for a home. We will default and use the Ysleta Independent School District tax rate for our school (more complete lookups will allow you to compute taxes based on exact address.) The taxing entities, and their respective tax rates per $100 is shown below:

Jurisdiction Total Rate ($) per $100

YSLETA ISD 1.3533

CITY OF EL PASO 0.907301

COUNTY OF EL PASO 0.488997

UNIVERSITY MEDICAL CENTER OF EL PASO 0.267747

EL PASO COMMUNITY COLLEGE 0.141167

Python Script Instructions: Create a loop that will allow the user to input a property value and calculate its related tax payment. Output property information as described below. The user will be asked to continue for another property or quit.

This will be a script broken into functions. It must include (may include more):

• Main function • Calculate property tax function

• Output information function called from Calculate function. Output will include the amount for each jurisdiction, and amount owed per year.

Other important information: We will assume each property value is eligible for a 10% Homestead Exemption of the property’s value. For example, if a property value is $100,000, the person would receive an exemption of $10,000. Their property taxes would be calculated on $90,000.

Don’t forget the rate is applied per $100 (i.e. you have to divide the amount for each jurisdiction you calculated by 100)

Sample calculation: Property value: $175,000 Yearly taxes owed: $4,974.66

Construction industry is considered as mother of all industries. It is industry of many industries. It is labor intensive and has the lowest capital cost for job creation. Pakistan is 6th largest country in terms of population with high rate of migration from rural to urban centers. According to one estimate about one-half of the households in urban area do not have their own house. There is therefore a great untapped potential for construction industry in the country The government in an effort to fulfill its promise of providing houses and creating employment opportunities has recently declared construction as an industry. It has offered several incentives to builders besides giving amnesty on investment that is the source of income will not be asked from the buyers and investors in the industry.
Required:
a-   Explain in brief the volume and value scope of construction industry in Pakistan.
b-   While explaining the economic importance highlight the socio-economic role of construction industry.
c-   Do you think that the package announced for construction industry is effective enough to boost the in industry? If yes/No, explain why?

virtual team. Chances are that you will be working some day in a virtual team, and most of you will also be assigned to be the leader of that virtual team. Chances are even greater because the corona virus has changed the world. But virtual teams are very difficult to lead because when there is no face-to-face interaction, then social dynamics do not develop (remember that listing the social dynamics [roles, norms, cohesion...] : how can a leader make a virtual team work effectively?

Question

(A) research virtual teams, so that you can understand them, (B) then develop a hypothesis on what the virtual team leader can do to make a virtual team become effective, then (C) apply your hypothesis to an example (real or imagined)

It is known that the duration of trouble-free operation of a new vacuum cleaner is normally distributed with a standard deviation of 98 days. The research department randomly selects 25 customers who bought these vacuum cleaners and records the duration of trouble-free operation to construct a 95% confidence interval for population mean duration of trouble-free operation. The critical value needed is _________ a. 1.96 b. 1.645 c. 2.064 d. Insufficient information to compute the critical value

A rock is thrown downward from a tower with an initial speed of 32.2 m/s. If it hits the ground in under 2 seconds how high is the tower?

I have some chemistry questions. please get all the answers correct ;)

a) Calculate the standard cell potential for the following cell

Zn (s) | Zn²⁺ (aq) (1M) || Co²⁺ (aq) (1M) | Co (s)

answer = __________V

b) The following cell was constructed and found to produce a voltage of 1.08 V.

Co (s) | Co²⁺ (aq) (1M) || Ag⁺ (aq) (1M) | Ag (s)

Calculate the standard reduction potential for Ag⁺ (aq) | Ag (s)

answer = _______V

c) Which of these species is the best oxidising agent?

Standard Reduction Potentials

Cu²⁺ | Cu    +0.34V

Ni²⁺ | Ni     �0.24V

Co²⁺ | Co    �0.28V

Fe²⁺ | Fe        �0.44V

Zn²⁺ | Zn    �0.76V

Mg²⁺ | Mg       �2.36V

Explain the difference between weak-field and strong-field metal complexes.

(around 200 words please)