A sample of n=18 observations is drawn from a normal population with μ=1040 and σ=230. Find each of the following:

A. P(X¯>1159)

Probability =

B. P(X¯<953)

Probability =

C. P(X¯>996)

Probability =

In 2019, Pittsburgh Steelers starting quarterback Ben Roethlisberger suffered a season-ending elbow injury in Week 2. The team struggled to find a quarterback until Week 12, when undrafted rookie Devlin “Duck” Hodges entered a game against the Cincinnati Bengals at halftime and led the Steelers to a surprising comeback victory. His performance earned him the starting job for the rest of the season and engendered a flurry of media speculation about his potential as a future quarterback for the Steelers.

Assume quarterbacks can either be good, average, or bad. Because Hodges was undrafted, it’s fair to say that coaches and fans had low expectations for him. Assume the initial probability distribution for Hodges was:

P(Good) =0.1

P(Average)=0.2

P(Bad)= 0.7

Also assume quarterbacks can either have strong performances or weak performances (there are only two types of performances, strong or weak). The chance of a good quarterback having a strong performance is 80%, the chance of an average QB having a strong performance is 50%, and the chance of a bad QB having a strong performance is 30%. We have:

P(S | G) =0.8

P(S | A)=0.5

P(S | B)= 0.3

From ESPN.com, Hodges turned in the following performances during the last 6 weeks of the season:

Use Bayes’s Rule to fill in the following table with the week-by-week probabilities of Duck being good, average, or bad.

In 2019, Pittsburgh Steelers starting quarterback Ben Roethlisberger suffered a season-ending elbow injury in Week 2. The team struggled to find a quarterback until Week 12, when undrafted rookie Devlin “Duck” Hodges entered a game against the Cincinnati Bengals at halftime and led the Steelers to a surprising comeback victory. His performance earned him the starting job for the rest of the season and engendered a flurry of media speculation about his potential as a future quarterback for the Steelers.

Assume quarterbacks can either be good, average, or bad. Because Hodges was undrafted, it’s fair to say that coaches and fans had low expectations for him. Assume the initial probability distribution for Hodges was:

P(Good) =0.1

P(Average)=0.2

P(Bad)= 0.7

Also assume quarterbacks can either have strong performances or weak performances (there are only two types of performances, strong or weak). The chance of a good quarterback having a strong performance is 80%, the chance of an average QB having a strong performance is 50%, and the chance of a bad QB having a strong performance is 30%. We have:

P(S | G) =0.8

P(S | A)=0.5

P(S | B)= 0.3

From ESPN.com, Hodges turned in the following performances during the last 6 weeks of the season:

Use Bayes’s Rule to fill in the following table with the week-by-week probabilities of Duck being good, average, or bad.

P9-3A On January 1, 2014, Pele Company purchased the following two machines for use in its production process. Machine A: The cash price of this machine was R$35,000. Related expenditures included: sales tax R$1,700, shipping costs R$150, insurance during shipping R$80, installation and testing costs R$70, and R$100 of oil and lubricants to be used with the machinery during its fi rst year of operations. Pele estimates that the useful life of the machine is 5 years with a R$5,000 residual value remaining at the end of that time period. Assume that the straight-line method of depreciation is used. Machine B: The recorded cost of this machine was R$80,000. Pele estimates that the useful life of the machine is 4 years with a R$5,000 residual value remaining at the end of that time period. Instructions (a) Prepare the following for Machine A. (1) The journal entry to record its purchase on January 1, 2014. (2) The journal entry to record annual depreciation at December 31, 2014. (b) Calculate the amount of depreciation expense that Pele should record for Machine B each year of its useful life under the following assumptions. (1) Pele uses the straight-line method of depreciation. (2) Pele uses the declining-balance method. The rate used is twice the straight-line rate. (3) Pele uses the units-of-activity method and estimates that the useful life of the machine is 125,000 units. Actual usage is as follows: 2014, 42,000 units; 2015, 35,000 units; 2016, 28,000 units; 2017, 20,000 units. (c) Which method used to calculate depreciation on Machine B reports the highest amount of depreciation expense in year 1 (2014)? The highest amount in year 4 (2017)? The highest total amount over the 4-year period?

DATA AND RESULTS

Mass of Ball: .059 kg

1. The potential energy of the object at its highest point _2.32_Trial #1

2. The kinetic energy of the object just before impact _2.32 _

3. The velocity of the object just before impact, using kinetic energy _8.87 _

4. The “kinetic energy” of the object just after impact _33.80_ (Hint: neglect air resistance and think about the height it rebounds to)

5. The “rebound” velocity of the object _10.62_

6. The loss in energy _0 + 2.32 = 33.80 + 0 + loss_

Trial #2

1. The potential energy of the object at its highest point _2.03_

2. The kinetic energy of the object just before impact _2.03_

3. The velocity of the object just before impact, using kinetic energy _8.30 _

4. The “kinetic energy” of the object just after impact _-32.97_

5. The “rebound” velocity of the object __

6. The loss in energy __

Trial #3

1. The potential energy of the object at its highest point _1.74_

2. The kinetic energy of the object just before impact _1.74_

3. The velocity of the object just before impact, using kinetic energy _7.68 _

4. The “kinetic energy” of the object just after impact _-1.28_

5. The “rebound” velocity of the object _6.59_

6. The loss in energy __

Can someone please help me on this to double check I am doing this correctly? Thank you!

Sales Territory and Salesperson Profitability Analysis

Havasu Off-Road Inc. manufactures and sells a variety of commercial vehicles in the Northeast and Southwest regions. There are two salespersons assigned to each territory. Higher commission rates go to the most experienced salespersons. The following sales statistics are available for each salesperson:

a. 1. Prepare a contribution margin by salesperson report. Compute the contribution margin ratio for each salesperson.

. 1. Prepare a contribution margin by territory report. Compute the contribution margin for each territory as a percent, rounded to one decimal place.

The Southwest Region has $_____???____ more sales and $____???_____ more contribution margin. In the Southwest Region, the salesperson with the highest sales unit volume, has the highest  contribution margin ratio. The Southwest Region has the highest  performance, even though it also has the salesperson with the lowest  contribution margin ratio. The Northeast Region contribution margin is less  than the Southwest Region because of the outstanding performance of Paul .

1. Wellness Data – Cholesterol levels.

Your worksite has instituted a new wellness program. As part of the plan for future evaluation of the effectiveness of the program, data are collected on a variety of health measures. These data are being collected every three months for the next two years. One of the measures collected by researchers was employee's cholesterol level. Initial data for 60 employees is listed below.

1. Find the highest and the lowest scores and place your data into an array, arranging values from highest to lowest

2. Evaluate your data. Do you see any clusters of scores, and are there any gaps in the data

3. Discuss your thoughts online as to what intervals should be used and why. Remember that your intervals must be equal and non-overlapping. Your intervals do NOT need to begin or end with your highest/lowest values.

4. After we have discussed the intervals, everyone should construct a frequency table for these data including intervals, frequency, relative frequency, and cumulative relative frequency and then create histograms and frequency polygons for these data.

5. Discuss online any problems you have in creating your tables and graphs as well as any questions you may have about the process.

Design a program that lets the user enter the total rainfall for each of 12 months into a list. The program should calculate and display the total rainfall for the year, the average monthly rainfall, the months with the highest and lowest amounts.

This is my Pthon 3.8.5 code so far:

#Determine Rainfall Program for a 12 month Period
#It should calculate and output the "total yearly rainfall, avg monthly rainfall, the months with highest and lowest amounts
#list of months in a year
months = ['January','February','March','April','May','June','July','August','September','October','November','December']
monthly_rain =[]
#functions to make calculations and inferences about rainfall within YEAR.
def average():
return total(monthly_rain)/len(months)
def total():
return sum(monthly_rain)
def HAVG():
return max(monthly_rain)
def LAVG():
return min(monthly_rain)
#UserInput
year = str(input('What year is this from: '))
for month in months:
monthly_rain.append(input('Enter the total rainfall for' + month + ' in cm: '))
rainfall = [str(monthly_rain) for int in monthly_rain]
print(year + 'Rainfall Chart')
print('MONTH | AVG RAINFALL')
print(months[0] + ' | ' + rainfall[0])
print(months[1] + ' | ' + rainfall[1])
print(months[2] + ' | ' + rainfall[2])
print(months[3] + ' | ' + rainfall[3])
print(months[4] + ' | ' + rainfall[4])
print(months[5] + ' | ' + rainfall[5])
print(months[6] + ' | ' + rainfall[6])
print(months[7] + ' | ' + rainfall[7])
print(months[8] + ' | ' + rainfall[8])
print(months[9] + ' | ' + rainfall[9])
print(months[10] + ' | ' + rainfall[10])
print(months[11] + ' | ' + rainfall[11])
print('--------------------------------------')
print('YEAR AVG: ' + str(average))
print('HIGHEST AVG: ' + str(HAVG) +' LOWEST AVG: ' + str(LAVG))

You are employed by a firm that manufactures computer chips. This firm receives components from two different suppliers. Currently, 65% of the components come from Supplier 1 and 35% of the components come from Supplier 2. Define A1 as the probability that a randomly-selected part comes from Supplier 1 and A2 as the probability that a randomly selected part comes from Supplier 2. In other words, Pr(A1) = .65 and Pr(A2) = .35.

Parts can be either good (G) or bad (B). We know from past experience that the probability that a part is bad varies based on the supplier it came from. Conditional on coming from Supplier 1, the probability that a part is good is .98, i.e. Pr(G | A1) = .98. The probability that a part is good, conditional on that part coming from Supplier 2 is .95, i.e. Pr(G | A2) = .95.

a.) What is the probability that any given part, chosen at random, is bad?

b.) What is the probability that of 5 chosen parts, at least one of the 5 parts will be bad?

c.) Suppose that you drew a part at random and discovered that it was bad. Your boss wants to know which supplier provided you the bad part. Calculate the probability that this bad part came from Supplier 1. Then calculate the probability that this bad part came from Supplier 2. Which supplier is more likely to have provided the bad part?

Question 1. Airports can be identified globally with a 3-digit letter code (e.g., YYZ for Toronto Pearson, and CDG for Charles de Gaulle in Paris). All possible combinations of letters A-Z can be used.

1a. What is the probability of selecting an airport at random and it being Montreal’s YUL?

1b. What is the probability of selecting one of London England’s six major airports?

1c. What is the probability of selecting an airport with two letter Y’s, (e.g., YYZ, YXY)?

1d. What is the probability of selecting an airport code where each letter is used only once (e.g., not YYZ, DBD, but something like LAX, LUA)?

1e. What percent of airport codes contain a letter that appears more than once?

1f. A frequent flyer has been to 305 different airports around the world. If you pick an airport at random, what is the probability that they have been to it?

1g. What is the probability of selecting one of Canada’s 518 airports?

1h. Interestingly, Canadian airports often start with a Y (e.g., YEG, YQX YHM). In fact, 88.61% of Canadian airports codes start with the letter Y. Given this information what is the probability that an airport code starting with Y is in Canada?

1i. In reference to 1g and 1h, if you select an airport code that does not start with the letter Y, what is the probability of it being in Canada?

1j. What is the probability of selecting an airport code which both starts with Y and is in Canada?