Jeff Heun, president of Marin Always, agrees to construct a concrete cart path at Dakota Golf Club. Marin Always enters into a contract with Dakota to construct the path for $181,000. In addition, as part of the contract, a performance bonus of $39,600 will be paid based on the timing of completion. The performance bonus will be paid fully if completed by the agreed-upon date. The performance bonus decreases by $9,900 per week for every week beyond the agreed-upon completion date. Jeff has been involved in a number of contracts that had performance bonuses as part of the agreement in the past. As a result, he is fairly confident that he will receive a good portion of the performance bonus. Jeff estimates, given the constraints of his schedule related to other jobs, that there is 60% probability that he will complete the project on time, a 25% probability that he will be 1 week late, and a 15% probability that he will be 2 weeks late.

Determine the transaction price that Marin Always should compute for this agreement.

Transaction Price: $

Assume that Jeff Heun has reviewed his work schedule and decided that it makes sense to complete this project on time. Assuming that he now believes that the probability for completing the project on time is 95% and otherwise it will be finished 1 week late, determine the transaction price.

Transaction Price: $

A project has four activities (A, B, C, and D) that must be performed sequentially. The probability distributions for the time required to complete each of the activities are as follows:

1. Provide the base-case, worst-case, and best-case calculations for the time to complete the project.
   

   Activity	Base case	Worst case	Best case
   A	weeks	weeks	weeks
   B	weeks	weeks	weeks
   C	weeks	weeks	weeks
   D	weeks	weeks	weeks
   Total	weeks	weeks	weeks

2. Use the random numbers 0.3487, 0.4561, 0.3031 and 0.9067 to simulate the completion time of the project in weeks.
   

   Activity	Random Number	Completion Time
   A	0.3487	weeks
   B	0.4561	weeks
   C	0.3031	weeks
   D	0.9067	weeks
   Total		weeks

3. Discuss how simulation could be used to estimate the probability that the project can be completed in weeks or less.
   
   Simulation provides a distribution of project completion times. The ___ of times weeks and under can be used to estimate the probability that the project will be completed within weeks.

1) A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 15.8 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 15.8 weeks and that the population standard deviation is 9.5 weeks. Suppose you would like to select a random sample of 22 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is between 19 and 20.7. P(19 < X < 20.7) =

Find the probability that a sample of size n = 22 n = 22 is randomly selected with a mean between 19 and 20.7. P(19 < M < 20.7) =

2)CNNBC recently reported that the mean annual cost of auto insurance is 995 dollars. Assume the standard deviation is 146 dollars. You will use a simple random sample of 138 auto insurance policies.

Find the probability that a single randomly selected policy has a mean value between 960.2 and 976.4 dollars.
P(960.2 < X < 976.4) =

Find the probability that a random sample of size n=138n=138 has a mean value between 960.2 and 976.4 dollars.
P(960.2 < M < 976.4) =

Enter your answers as numbers accurate to 4 decimal places.

Suppose the amount of time needed to change the oil in a car is uniformly distributed between 14 minutes and 30 minutes, with a mean of 22 minutes and a standard deviation of 4.6 minutes.

Let X represent the amount of time, in minutes, needed to complete a randomly selected oil change. What is the probability that a randomly selected oil change takes at most 20 minutes to complete?

Assuming a randomly selected oil change has already taken 18 minutes and it is still not complete, what is the probability that the oil change takes no more than 5 additional minutes to complete?

Find the value that best completes the following statement: The slowest 20% of oil changes take at least __________ minutes to complete. Suppose 3 oil changes are selected at random.

Let Y be defined as the number of oil changes that take more than 20 minutes to complete in a random sample of 3. What is the probability that exactly 2 of the 3 randomly selected oil changes take more than 20 minutes to complete?

Suppose 500 oil changes are selected at random. What model would you use to approximate the probability that at least 190 of the randomly selected oil changes take at most 20 minutes to complete? Provide the approximate model with corresponding parameters.

The Denver Post reported that, on average, a large shopping center had an incident of shoplifting caught by security 1.2 times every four hours. The shopping center is open from 10 A.M. to 9 P.M. (11 hours). Let r be the number of shoplifting incidents caught by security in an 11-hour period during which the center is open.

(a) Explain why the Poisson probability distribution would be a good choice for the random variable r.

1) Frequency of shoplifting is a rare occurrence. It is reasonable to assume the events are dependent.

2) Frequency of shoplifting is a common occurrence. It is reasonable to assume the events are dependent.   

3) Frequency of shoplifting is a rare occurrence. It is reasonable to assume the events are independent.

4) Frequency of shoplifting is a common occurrence. It is reasonable to assume the events are independent.

What is λ? (Use 2 decimal places.)


(b) What is the probability that from 10 A.M. to 9 P.M. there will be at least one shoplifting incident caught by security? (Use 4 decimal places.)


(c) What is the probability that from 10 A.M. to 9 P.M. there will be at least three shoplifting incidents caught by security? (Use 4 decimal places.)


(d) What is the probability that from 10 A.M. to 9 P.M. there will be no shoplifting incidents caught by security? (Use 4 decimal places.)

Strassel Investors buys real estate, develops it, and resells it for a profit. A new property is available, and Bud Strassel, the president and owner of Strassel Investors, believes if he purchases and develops this property it can then be sold for $160,000. The current property owner has asked for bids and stated that the property will be sold for the highest bid in excess of $100,000. Two competitors will be submitting bids for the property. Strassel does not know what the competitors will bid, but he assumes for planning purposes that the amount bid by each competitor will be uniformly distributed between $100,000 and $150,000.

Develop a worksheet that can be used to simulate the bids made by the two competitors. Strassel is considering a bid of $130,000 for the property. Using a simulation of 1000 trials, what is the estimate of the probability Strassel will be able to obtain the property using a bid of $130,000? Round your answer to 1 decimal place. Enter your answer as a percent. ___________%

Use the simulation model to compute the profit for each trial of the simulation run. With maximization of profit as Strassel’s objective, use simulation to evaluate Strassel’s bid alternatives of $130,000, $140,000, or $150,000. What is the recommended bid, and what is the expected profit? A bid of $140,000 results in the largest mean profit of $ _________________.

Fill in needed code to finish Mastermind program in Python 3.7 syntax

Plays the game of Mastermind.
The computer chooses 4 colored pegs (the code) from the colors
Red, Green, Blue, Yellow, Turquoise, Magenta.
There can be more than one of each color, and order is important.

The player guesses a series of 4 colors (the guess).

The computer compares the guess to the code, and tells the player how
many colors in the guess are correct, and how many are in the correct
place in the code. The hint is printed as a 4-character string, where
* means correct color in correct place
o means correct color in incorrect place
- fills out remaining places to make 4

The player is allowed to make 12 guesses. If the player guesses the colors
in the correct order before all 12 guesses are used, the player wins.

'''

import random

def genCode(items, num):
'''
Generates a random code (a string of num characters)
from the characters available in the string of possible items.
Characters can be repeated

items - a string of the possible items for the code
num - the number of characters in the code
returns the code string
'''
# write function body here

def valid(guess, items, num):
'''
Checks a guess string to see that it is the correct length and composed
of valid characters.

guess - a string representing the guess
items - a string of the possible items for the code
num - the number of characters in the code
returns True if the guess is valid, False otherwise
'''
# write function body here

def getGuess(items, num):
'''
Gets a guess string from the user. If the guess is not valid length and
characters, keeps asking until the guess is valid.

items - a string of the possible items for the code
num - the number of characters in the code
returns the valid guess
'''
# write function body here

def matched(code, guess):
'''
Checks to see that the code and the guess match.

code - the string with the secret code
guess - the string with the player's guess
returns True if they match, False otherwise
'''
# write function body here

def genHint(code, guess, items, num):
'''
Generates a string representing the hint to the user.
Tells the player how many colors in the guess are correct,
and how many are in the correct place in the code.
The hint is printed as a num-character string, where
* means correct color in correct place
o means correct color in incorrect place
- fills out remaining places to make num

code - the string with the secret code
guess - the string with the player's guess
items - a string of the possible items for the code
num - the number of characters in the code/hint
returns the valid hint as a string
'''
# write function body here

# Main program starts here

# colors for the code
colors = 'RGBYTM'
# length of the code
num = 4
# maximum number of guesses allowed
maxGuesses = 12

print('Plays the game of Mastermind.')
print()
print('The computer chooses', num, 'colored pegs (the code) from the colors')
print(colors)
print('There can be more than one of each color, and order is important.')
print()
print('The player guesses a series of', num, 'colors (the guess).')
print()
print('The computer compares the guess to the code, and tells the player how')
print('many colors in the guess are correct, and how many are in the correct')
print('place in the code. The hint is printed as a', num, '-character string, where')
print(' * means correct color in correct place')
print(' o means correct color in incorrect place')
print(' - fills out remaining places to make', num)
print()
print('The player is allowed to make', maxGuesses, 'guesses. If the player guesses the colors')
print('in the correct order before all', maxGuesses, 'guesses are used, the player wins.')

gameOver = False
guesses = 0

code = genCode(colors, num)

while not gameOver:
guess = getGuess(colors, num)
guesses = guesses + 1
  
if matched(code, guess):
print('You win!')
gameOver = True
continue
  
hint = genHint(code, guess, colors, num)
print(hint)

if guesses == maxGuesses:
print('You took to many guesses. The code was', code)
gameOver = True

Suppose that an insurance company sells a policy whose losses are distributed exponentially with mean $1500. Further suppose that the company sells a large number of claims. An actuary wishes to analyze the performance of the product and takes a random sample of 100 policies for which there was a claim filed from this population.

a. What are the mean and variance of an individual insurance policy?

b. What are the mean and variance of the total claim amount T of these 100 selected policies?

c. What are the mean and variance of the average claim amount ?̅ = ?/100 of these 100 policies?

d. Calculate the approximate probability that the total claim amount T from the sample is between $160,000 and $170,000?

e. Calculate the approximate probability that the average claim ?̅ from the sample exceeds $1700.

f. What average claim amount will 18.67% of sample means exceed based on the information above?

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 40 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 40 weeks and that the population standard deviation is 3.2 weeks. Suppose you would like to select a random sample of 79 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is greater than 40.6. P(X > 40.6) = (Enter your answers as numbers accurate to 4 decimal places.)

Find the probability that a sample of size n = 79 n = 79 is randomly selected with a mean greater than 40.6. P(M > 40.6) =

(Enter your answers as numbers accurate to 4 decimal places.)