Probability and descriptive statistics are used all around us (think: life expectancy, batting averages, chances of rain, election results, sales, and lottery tickets). Both give us an opportunity to analyze data and are especially useful for making decisions. Each of the following problems will assess your ability to use basic probability and descriptive statistics to solve real-world quantitative problems.
1. Read the scenario and use your knowledge of probability to answer the prompt in the text box below the assignment. (20 points)
Scenario: You are the marketing manager at The Best Candy Shop where the top sales item is the Dream Pop bags of flavored candies. You have been getting complaints from customers that there are not enough lemon or blueberry-flavored candies, which are favorites, and too many grape and strawberry-flavored candies. Your boss wants you to create an advertisement indicating, “All bags have equally likely flavors.” (That is, the probability of getting a strawberry-flavored candy piece is the same as getting a blueberry-flavored candy piece, etc.).
As the marketing manager, you want to make sure you are advertising truthful information, so you pull a sample bag of Dream Pop candy and find the following pieces:
14 grape flavors
10 strawberry flavors
8 lemon flavors
8 blueberry flavors
Calculate the probability of getting each flavor in the pack (explain how you found the probability of each: grape, strawberry, lemon, and blueberry). Using those probability values, explain to your boss why his advertising suggestion (that all bags have equally likely flavors) is incorrect.
2. Read the scenario and use your knowledge of descriptive statistics to answer parts A and B in the text box below the assignment. (20 points)
Scenario: Customers at IT Phone Call Center have been complaining that they are waiting too long for service. The managers at the call center have taken notice and asked you to do some investigating to determine the typical service time for their customers for morning shifts compared to evening shifts. You collect the following samples (time in minutes):
Morning shifts: 7,14,15,17,17,19,20,20,20,55
Evening shifts: 2,10,11,13,21,21,29,32,33,46
Calculate the mean, median, and mode for each shift using the data above. Explain your calculations.
Determine which descriptive statistic (mean, median, or mode) you would utilize to communicate the typical service time to your boss for each shift and why. In your explanation, be sure to include which shift (morning or evening) has the quicker turn-around time.
Dante Alighieri played a critical role in the literature world through his poem Divine Comedy that was written in the 14th century. The poem contains Inferno, Purgatorio, and Paradiso. The Inferno is a description of the nine circles of torment that are found on the earth. It depicts the realms of the people that have gone against the spiritual values and who, instead, have chosen bestial appetite, violence, or fraud and malice. The nine circles of hell are limbo, lust, gluttony, greed and wrath. Others are heresy, violence, fraud, and treachery. The purpose of this paper is to examine the Dante’s Inferno in the perspective of its portrayal of God’s image and the justification of hell.
In this epic poem, God is portrayed as a super being guilty of multiple weaknesses including being egotistic, unjust, and hypocritical. Dante, in this poem, depicts God as being more human than divine by challenging God’s omnipotence. Additionally, the manner in which Dante describes Hell is in full contradiction to the morals of God as written in the Bible. When god arranges Hell to flatter Himself, He commits egotism, a sin that is common among human beings (Cheney, 2016). The weakness is depicted in Limbo and on the Gate of Hell where, for instance, God sends those who do not worship Him to Hell. This implies that failure to worship Him is a sin.
God is also depicted as lacking justice in His actions thus removing the godly image. The injustice is portrayed by the manner in which the sodomites and opportunists are treated. The opportunists are subjected to banner chasing in their lives after death followed by being stung by insects and maggots. They are known to having done neither good nor bad during their lifetimes and, therefore, justice could have demanded that they be granted a neutral punishment having lived a neutral life. The sodomites are also punished unfairly by God when Brunetto Lattini is condemned to hell despite being a good leader (Babor, T. F., McGovern, T., & Robaina, K. (2017). While he commited sodomy, God chooses to ignore all the other good deeds that Brunetto did.
Finally, God is also portrayed as being hypocritical in His actions, a sin that further diminishes His godliness and makes Him more human. A case in point is when God condemns the sin of egotism and goes ahead to commit it repeatedly. Proverbs 29:23 states that “arrogance will bring your downfall, but if you are humble, you will be respected.” When Slattery condemns Dante’s human state as being weak, doubtful, and limited, he is proving God’s hypocrisy because He is also human (Verdicchio, 2015). The actions of God in Hell as portrayed by Dante are inconsistent with the Biblical literature. Both Dante and God are prone to making mistakes, something common among human beings thus making God more human.
To wrap it up, Dante portrays God is more human since He commits the same sins that humans commit: egotism, hypocrisy, and injustice. Hell is justified as being a destination for victims of the mistakes committed by God. The Hell is presented as being a totally different place as compared to what is written about it in the Bible. As a result, reading through the text gives an image of God who is prone to the very mistakes common to humans thus ripping Him off His lofty status of divine and, instead, making Him a mere human. Whether or not Dante did it intentionally is subject to debate but one thing is clear in the poem: the misconstrued notion of God is revealed to future generations.
References
Babor, T. F., McGovern, T., & Robaina, K. (2017). Dante’s inferno: Seven deadly sins in scientific publishing and how to avoid them. Addiction Science: A Guide for the Perplexed, 267.
Cheney, L. D. G. (2016). Illustrations for Dante’s Inferno: A Comparative Study of Sandro Botticelli, Giovanni Stradano, and Federico Zuccaro. Cultural and Religious Studies, 4(8), 487.
Verdicchio, M. (2015). Irony and Desire in Dante’s” Inferno” 27. Italica, 285-297.
Problem 1: Candy Probabilities
Calculating Probabilities:
- Total candies: 14 + 10 + 8 + 8 = 40
- Probability of grape: 14/40 = 0.35
- Probability of strawberry: 10/40 = 0.25
- Probability of lemon: 8/40 = 0.20
- Probability of blueberry: 8/40 = 0.20
Explanation:
To calculate the probability of a specific flavor, we divide the number of candies of that flavor by the total number of candies in the bag. As we can see, the probabilities are not equal, meaning the flavors are not equally likely. Therefore, the boss’s suggestion to advertise “equally likely flavors” is incorrect.
Problem 1: Candy Probabilities
Calculating Probabilities:
- Total candies: 14 + 10 + 8 + 8 = 40
- Probability of grape: 14/40 = 0.35
- Probability of strawberry: 10/40 = 0.25
- Probability of lemon: 8/40 = 0.20
- Probability of blueberry: 8/40 = 0.20
Explanation:
To calculate the probability of a specific flavor, we divide the number of candies of that flavor by the total number of candies in the bag. As we can see, the probabilities are not equal, meaning the flavors are not equally likely. Therefore, the boss’s suggestion to advertise “equally likely flavors” is incorrect.
Problem 2: Descriptive Statistics for Call Center Service Times
A. Calculating Mean, Median, and Mode:
Morning Shift:
- Mean: (7+14+15+17+17+19+20+20+20+55)/10 = 19.4 minutes
- Median: Arrange the data in ascending order: 7, 14, 15, 17, 17, 19, 20, 20, 20, 55. The median is the middle value, which is the average of the 5th and 6th values: (17+19)/2 = 18 minutes.
- Mode: The most frequent value is 20, so the mode is 20 minutes.
Evening Shift:
- Mean: (2+10+11+13+21+21+29+32+33+46)/10 = 21.8 minutes
- Median: Arrange the data in ascending order: 2, 10, 11, 13, 21, 21, 29, 32, 33, 46. The median is the average of the 5th and 6th values: (21+21)/2 = 21 minutes.
- Mode: The most frequent value is 21, so the mode is 21 minutes.
B. Choosing the Best Descriptive Statistic:
- Morning Shift: The median would be the best statistic to communicate the typical service time. This is because the mean is skewed upward by the outlier value of 55. The median, on the other hand, is not affected by outliers.
- Evening Shift: The mean could be used to represent the typical service time, as there are no significant outliers in this data set.
Conclusion: Based on the median service time, the morning shift has a quicker turnaround time compared to the evening shift.
