Engineer E and Owner O are engaged in contract negotiations for E to design and build a building for O. The proposed contract is for $200,000. The estimated duration of the turnkey project is 15 months. After reaching an oral agreement of the above, O tells E that they should get together over the next few weeks to hammer out the contract language details for a formal written contract. E begins work without notifying O and completes approximately 30% of the design work (at a cost of $3000) when negotiations break off over "technicalities." When E indicates work has already begun, O orally tells E to stop work as they cannot reach an agreement. E's budget estimated a $12,000 profit for E for the project. Assume for this question that the design/build turnkey project is NOT severable.

1. E sues O for the entire $200,000. Who wins, what, and why?

2. ADDITIONAL FACTS: O mails a check for $3,000 to E with a letter stating that the check is "to cover your costs for the work performed under our canceled agreement for the $150,000 project." E sues O for the remaining $197,000. O countersues asking for the return of the $3,000. Who wins, what, and why?

1.

Mrs. Walker filled out a bracket for the NCAA National Tournament. Based on her knowledge of college basketball, she has a 0.53 probability of guessing any one game correctly.

What is the probability Mrs. Walker will pick all 32 of the first round games correctly?

What is the probability Mrs. Walker will pick exactly 10 games correctly in the first round?

What is the probability Mrs. Walker will pick exactly 20 games incorrectly in the first round?

2.

After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only five women among the last 19 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men as qualified women.

Help her address the charge of gender discrimination by finding the probability of getting five or fewer women when 19 people are hired, assuming that there is no discrimination based on gender.
(Report answer accurate to 8 decimal places).
P(at most five) =

thank you

"What do you think is the ideal number of children for a family to have?" A Gallup Poll asked this question of 1016 randomly chosen adults. Almost half (49%) thought two children was ideal.† We are supposing that the proportion of all adults who think that two children is ideal is p = 0.49.
What is the probability that a sample proportion p̂ falls between 0.46 and 0.52 (that is, within ±3 percentage points of the true p) if the sample is an SRS of size n = 300? (Round your answer to four decimal places.)


What is the probability that a sample proportion p̂ falls between 0.46 and 0.52 if the sample is an SRS of size n = 5000?(Round your answer to four decimal places.)


Combine these results to make a general statement about the effect of larger samples in a sample survey.

Larger samples give a smaller probability that p̂ will be close to the true proportion p.Larger samples have no effect on the probability that p̂ will be close to the true proportion p.    Larger samples give a larger probability that p̂ will be close to the true proportion

The number N of devices that a technician must try to repair during the course of an arbitrary workday is a random variable having a geometric distribution with parameter p = 1/8. We estimate the probability that he manages to repair a given device to be equal to 0.95, independently from one device to another

a) What is the probability that the technician manages to repair exactly five devices, before his second failure, during a given workday, if we assume that he will receive at least seven out-of-order devices in the course of this particular workday?

b) If, in the course of a given workday, the technician received exactly ten devices for repair, what is the probability that he managed to repair exactly eight of those?

c) Use a Poisson distribution to calculate approximately the probability in part (b).

d) Suppose that exactly eight of the ten devices in part (b) have indeed been repaired. If we take three devices at random and without replacement among the ten that the technician had to repair, what is the probability that the two devices he could not repair are among those?

The traffic volume in the year 2018 at an airport (number of take-offs and landings) during peak hour of each day is a described as a log-normal random variable with a mean of 200 planes and a standard deviation of 60 planes. a. If the present runway capacity (for landings and take-offs) is 350 planes per hour, what is the current probability of congestion? [2 marks] b. If the mean traffic volume is increasing linearly at the annual rate of 10% of the volume in 2018 with the coefficient of variation remaining constant what would be the probability of congestion at the airport in year 2028? [2 marks] c. Assuming the same projected growth rate of traffic volume as part (b), and that the maximum acceptable probability of congestion is 10% what year will the airport need to increase their runway capacity? [4 marks] d. Assuming the same projected growth rate of traffic volume as part (b) when the airport upgrades their runway capacity in part (c) what new runaway capacity will they need to ensure the probability of congestion does not exceed the max acceptable probability of congestion of 10% until year 2038? [2 marks]

A survey showed that 78% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 9 adults are randomly selected, find the probability that at leastat least 8 of them need correction for their eyesight. Is 8 a significantly highhigh number of adults requiring eyesight correction?

A fair six-sided die is rolled repeatedly until the third time a 6 is rolled. Let X denote the number of rolls required until the third 6 is rolled. Find the probability that fewer than 5 rolls will be required to roll a 6 three times.

It has been reported that 42% of college students graduate in 4 years. Consider a random sample of thirty students, and let the random variable X be the number who graduate in 4 years.

Find the probability that 14 or fewer students in the sample graduate in 4 years.

The number X of cars that Linda hopes to sell has the distribution:

Cars sold    0   1    2   3

Probability 0.2 0.1      0.3    0.4

Find the mean and standard deviation of X.

Five cards are dealt from a standard 52 card deck

1. Determine the number of possible outcomes we could obtain
2. What is the probability we draw
   1. Any flush (five cards of same suit)
   2. Four of a kind ( four cards of all the same rank)