Must show all needed steps in getting to your final answer. And, express your final answer as a decimal.

Show every step NEATLY please

NEATLY AND VERY CLEAR AND READABLE

PLEASE TYPE ANSWER AND WORK

NEATLY AND VERY CLEAR AND READABLE

PLEASE TYPE ANSWER AND WORK

Part 1) Suppose that you are planning to travel a certain air route via plane once each week for your new job. Also, assume that there is a 3% chance that your outbound flight may be cancelled on any given week due to various issues. How many consecutive outbound weekly flights can you fly before the probability of another successful flight (that is, a flight that is not cancelled) drops to 50% or less?

Part 2) Assume that you are playing a game in which you pull a lever and a light comes on. The light will be either red or green. Assume that on any given pull of the lever, P(Red Light) = .40 and P(Green Light) = .60. Find the probability that in pulling the lever 5 times that you will get your 3rd Green Light on the 5th pull of the lever.

Part 3) Suppose in front of you are three boxes that look identical. Further, you are told that one box contains two $1 bills, one contains two $100 bills, and one contains one $1 bill and one $100 bill. You are permitted to choose one box. Then you are asked to remove one bill from the box you chose without looking at the other bill in that box. Suppose that a $100 bill comes out. What is the probability that the other bill in that box is $100?

1. A poll is given, showing 20% are in favor of a new building project.
If 10 people are chosen at random, what is the probability that exactly 4 of them favor the new building project?

2. According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. You randomly select six peanut M&M’s from an extra-large bag of the candies. (Round all probabilities below to four decimal places; i.e. your answer should look like 0.1234, not 0.1234444 or 12.34%.)
a.) Compute the probability that exactly two of the six M&M’s are yellow.
b.) Compute the probability that two or three of the six M&M’s are yellow.
c.) Compute the probability that at most two of the six M&M’s are yellow.
d.) Compute the probability that at least two of the six M&M’s are yellow.

3. A small regional carrier accepted 11 reservations for a particular flight with 10 seats. 7 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 40% chance, independently of each other.
a.) Find the probability that overbooking occurs.
b.) Find the probability that the flight has empty seats

4. The Smith family was one of the first to come to the U.S. They had 7 children. Assuming that the probability of a child being a girl is .5, find the probability that the Smith family had:a.) at least 3 girls?
b.) at most 3 girls?

5. A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.14.
• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 3 tornadoes in a 10-year period.

Please write a program in c++ The method sellProduct of the Juice Machine programming example gives the user only two chances to enter enough money to buy the product. Rewrite the definition of the method sellProduct so that it keeps prompting the user to enter more money as long as the user has not entered enough money to buy the product. Also, write a program to test your method.

Your program should produce the following example output:

*** Welcome to Shelly's Juice Shop ***                               
To select an item, enter                                             
1 for orange juice (50 cents)                                        
2 for apple juice (65 cents)                                         
3 for mango juice (80 cents)                                         
4 for strawberry banana juice (85 cents)                             
9 to exit                                                            
3                                                                    
Please deposit 80 cents                                              
40                                                                   
Please deposit another 40 cents.                                     
40                                                                   
Collect your item at the bottom and enjoy.                           
*** Welcome to Shelly's Juice Shop ***                               
To select an item, enter                                             
1 for orange juice (50 cents)                                        
2 for apple juice (65 cents)                                         
3 for mango juice (80 cents)                                         
4 for strawberry banana juice (85 cents)                             
9 to exit                                                            
9

The Haynesworth Corporation is sued for $10 million in Year One. At the end of Year One, company officials believe a loss is only remote. However, the case drags on so that by the end of Year Two, company officials believe it is reasonably possible that a loss of $2 million could be incurred. The case goes to trial during Year Three, and company officials now believe that a loss of $3 million is probable. The case ends on April 23, Year Four, when the Haynesworth Corporation agrees to pay $2.6 million in cash to settle all claims. Indicate the amount of loss that will be reported by the Haynesworth Corporation in each of these four years. 6. On January 1, Year One, the Atlanta Company sues the Seattle Company for $100 million for patent infringement. The case is expected to take years to settle. For each of the following independent situations, indicate the financial reporting to be made by each company. a. Both companies believe that Atlanta will probably win this case. However, both feel that estimating the amount of this loss is virtually impossible. b. Both companies believe that Atlanta will probably win this case. Both feel that Atlanta will probably win approximately $9 million, but a win as high as $46 million is reasonably possible. c. Both companies believe that a loss by Seattle of $53 million is reasonably possible. d. Atlanta officials believe that their company will probably win $44 million whereas Seattle officials believe that their company will probably lose $8 million.

Use this mini-case to answer the following question(s). (Total marks = 100)
The Delux Nut Company produces a deluxe mix of almonds, cashews, peanuts and walnuts. The deluxe mix must contain at least 10% of each kind of nut. At least half of the mix must consist of almonds and cashews and it can contain at most 20% peanuts.
The company also produces a companion mix of cashews, walnuts and raisins. This mix must contain at least 10% cashews, at least 30% walnuts, and between 20 and 40% raisins. Raisins are available in unlimited supply at a purchasing cost of R3,60 per kilogram. The quantities of nuts available and the purchasing costs in rand per kilogram are as follows:

Both mixes are sold in 100 g packages. The company must produce at least 4 000 packages of the deluxe mix and at least 5 000 packages of the companion mix.
(a) Formulate an LP model for this problem.
(b) Solve the LP using SOLVER (NB: Please use solver for me and not LINGO)
(c) Write down the optimal purchasing plan and the associated purchasing costs.

Use only the initial printout of the optimal solution to answer the following questions. (This means that you may not change the relevant parameters in the model and do re-runs.) Explain how you arrive at your answers.
(d) The suppliers inform the company that the availability of almonds has been reduced to 200 kg and that of peanuts to 100 kg. How will this influence the optimal plan and purchasing costs? Give reasons for your answer.
(e) An extra 50 kg of walnuts can be bought at R11,00 per kg. Would you make use of this offer? Give reasons for your answer.
(f) Assume that the optimal plan is obtained from the original available quantities of nuts. The company now decides that it must produce at least 4 500 packages of the deluxe mix. Will the total purchasing costs be influenced? Give reasons for your answer.
(g) The supplier of peanuts announces a 40% increase in price. What will the effect of this be? Give reasons for your answer.

Assume the following list of keys:

78, 40, 16, 82, 64, 67, 57, 40, 37, 47, 72, 14, 17, 27, 55

This list is to be sorted using the quick sort algorithm as discussed in this chapter. Use pivot as the median of the first, last, and middle elements of the list.

1. What is the pivot?
2. Give the resulting list after one call to the partition function.

Align two sequences shown below using Needelman Wunsch algorithm. Use match score of 3, mismatch score of -3 and gap penalty score of 2 (note, you should subtract this from the scoring function).

Show:

a) dynamic programming matrix with scores

b) trace back pointers

c) alignment score sequences:

sequence 1: AGAGCTCACAA

sequence 2: AGTAGCTTCCAAA

Two investments with varying cash flows (in thousands of dollars) are available, as shown in Table. At time 0, $10,000 is available for investment, and at time 1, $7,000 is available.

Investment 0 1 2 3

A -6 -5 7 9

B -8 -3 9 7

Assuming that r = 0.40 (4%), set up an LP whose solution maximizes the NPV obtained from these investments. Graphically find the optimal solution to the LP.

Resuelva cada uno de los ejercicios de pruebas de hipótesis usando Excel o R:Las universidades A y B se preguntan si el nivel formativo en estadística de una y otra universidad es diferente. Para tratar de dar respuesta a esta pregunta, someten a 75 alumnos de cada universidad elegidos al azar a un mismo examen. Las calificaciones de los alumnos de cada universidad pueden verse en las columnas A y B respectivamente de este archivo (enlace). Supuestos del modelo t de Student que debe verificar antes de aplicar la prueba. Distribución: normal o aproximadamente normal. Varianzas poblacionales: desconocidas, supuestamente iguales o sin supuesto de igualdad. Observaciones: aleatorias e independientes. Hipótesis que se somete a prueba: la diferencia entre las dos medias toma un determinado valor, generalmente cero.

Universidad A

39        31        28        26        18        25        23        41        18        36        30        49        17        27        34        47        40        33        26        41        37        27        47        50        42        32        39        19        19        35        31        37        27        32        34        17        38        47        14        34        24        31        23        28        22        49        34        23        46        32        32        42        45        31        47        25        35        24        28        39        39        49        34        30        25        30        38        19        31        35        31        41        45        45        18     Universidad B

40        14        25        21        33        33        26        44        28        42        37        23        44        25        36        33        37        44        11        32        23        29        25        20        33        21        35        20        14        22        45        28        34        48        22        22        30        41        39        23        24        27        34        35        20        38        30        40        45        22        39        37        47        40        32        32        19         30        29        41        36        24        31        27        33        39        30        34        24        19        41        31        30        41        38

A sample of 81 60-watt lightbulbs produced by Dynamics, Inc. obtained a mean lifetime of 1347 hours with a variance of 729 hours. A sample of 50 60-watt lightbulbs produced by National Electronics Corporation obtained a mean lifetime of 1282 hours with a variance of 800 hours.

a) Calculate a 99% confidence interval for μ1- μ2, the difference between the true mean lifetimes of the two type of lightbulbs. Answer to one decimal place, the lower bound and the upper bound of the interval should be correct to one decimal place.

b) Test H₀: μ₁- μ₂ = 50 versus H₁ : μ₁- μ₂ > 50 by setting α = .01 . We can reject the Null Hypothesis.

True or False?