Series of observations find the mean, median, and midrange

by | Oct 28, 2022 | mathematics

 

1. For the following series of observations find the mean, median, and midrange.
6, 5, 2, 11, 5, 3, 9, 13, 20, 5, 16, 1.
2. Suppose your instructor assigns grade for the course based on your performance as following: 35% for quizzes, 25% for midterm exam, 35% for final exam, and 5% for attendance and class participation. What would your grade score be if you scored 75 points on quizzes, 80 points on midterm exam, 85 points on your final exam, and 90 points on attendance and class participation? (Calculate mean value from the following probability table). Round your answer to the nearest integer.
Quizzes Midterm Exam Final Exam Attendance
Scores, X 75 80 85 90
Probability, P(X) 0.35 0.25 0.35 0.05
μ =
– 2 –
Use Binomial Distribution to solve problems 3 – 4
3. Over a long period of time a certain drug has been effective in 80% of the cases in which it has been prescribed. If a doctor is now administering this drug to five patients, what is the probability that it will be effective for
a) one patient
P(X = 1) =
b) less than two patients
P(X < 2) =
4. If 40% of employees in the company are females and 6 employees are randomly chosen to serve on a committee, what is the probability that:
a) No women will be selected
P(X=0) =
b) One or more women will be selected
P(X ≥ 2)
Use Poisson Distribution to solve problem 5
5. The expected number of typographical errors on a page of a certain magazine is 2.75
What is the probability that the next page you read contains more than 1 typographical error:
P(X >1) =
– 3 –
Use Normal Distribution to solve problems 6–8
6. If Z is a standard normal variable find the probabilities of:
a) P(Z < −1.68) =
b) P(−1.68< Z < 1.89) =
c) P(Z > 1.89) =
7. It is said that sufferers of a cold virus experience symptoms for 7 days. However, the amount of time is a normally distributed random variable whose mean is 7.5 days and whose standard deviation is 1.2 days.
What proportion of cold sufferers experiences symptoms for between 7 and 10 days?
P(7 < X < 10 ) =
8. The weekly salaries of teachers in one state are normally distributed with a mean of $1850 and a standard deviation of $75. What is the amount of money that separates
a) bottom 3% of these teachers
b) top 14% of these teachers

Sample solution

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.


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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.

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