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Descriptive Statistics and Probability

Research Paper Instructions:

Complete the following questions in a 1-3-page document formatted per the CSU Global Writing Center (Links to an external site.). Be sure to use Version 1 of Online Statistics: An Interactive Multimedia Course of Study.
Lane, Chapter 5, (Links to an external site.) exercises 13 25 (Coin, Insurance)
Lane, Chapter 6 (Links to an external site.), exercises 29 30 (Women, Automobile)
13. An unfair coin has a probability of coming up heads of 0.65. The coin is flipped 50 times. What is the probability it will come up heads 25 or fewer times? (Give answer to at least 3 decimal places).
25. An insurance company writes policies for a large number of newly-licensed drivers each year. Suppose 40% of these are low-risk drivers, 40% are moderate risk, and 20% are high risk. The company has no way to know which group any individual driver falls in when it writes the policies. None of the low-risk drivers will have an at-fault accident in the next year, but 10% of the moderate-risk and 20% of the high-risk drivers will have such an accident. If a driver has an at-fault accident in the next year, what is the probability that he or she is high-risk?
29. Heights of adult women in the United States are normally distributed with a population mean of μ = 63.5 inches and a population standard deviation of σ = 2.5. A medical researcher is planning to select a large random sample of adult women to participate in a future study. What is the standard value, or z-value, for an adult woman who has a height of 68.5 inches?
30. An automobile manufacturer introduces a new model that averages 27 miles per gallon in the city. A person who plans to purchase one of these new cars wrote the manufacturer for the details of the tests, and found out that the standard deviation is 3 miles per gallon. Assume that in-city mileage is approximately normally distributed.
What is the probability that the person will purchase a car that averages less than 20 miles per gallon for in-city driving?
What is the probability that the person will purchase a car that averages between 25 and 29 miles per gallon for in-city driving?

Research Paper Sample Content Preview:

Descriptive Statistics and Probability
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Descriptive Statistics and Probability
Question 13: Probability of unfair coin
The coin has a probability of 0.65 to turn head when flipped. Determining the probability of the coin to turn heads 25 or lesser times when flipped 50 times is the question. The probability in this question shall be determined as a normal distribution denoted by z. Therefore, the following formula shall be used to determine Z;
Z = (x-µ)/ σ where X= mean, µ is our corresponding probability denoted as (p)x and σ is the standard deviation of probability distribution. From the information provided we can get n = 50 (number of flips), p= 0.65 and q= 0.35 (probability of fail or Binomial probability). This information can therefore be used to obtain µ an σ where µ = np while σ= √(npq).
Therefore,µ = 50 x .65 = 32.5
σ = square root of 50 x .65 x .35 = 3.373
The probability of the coin turning heads 25 times or less is calculated by the formula (x-µ)/ σ, but to get x we subtract the corresponding probability which 32.5 from the corresponding n, which is ≤ 25.
Therefore 25 - 32.5= 7.5.
The probability of the coin turning heads 25 ties or less = (-7.5/3.373) =-2.224. Z is therefore -2.224. Using z table, probability of the coin turning head 25 or less times is 0.0131.
Question: Probability of high risk driver causing an at fault accident
In this question, the following abbreviations refers to the correspondent drivers as illustrated. LR- Low risk, MR- Moderate risk, HR-high risk and AFT- at fault accident. Therefore, probability of different categories of drivers are as follows:
P(LR)= (40/100) = 0.40
P(MR)= (40/100) = 0.40
P(HR)= (20/100) = 0.20
P(AFT:LR)= (0/100) = 0
P(AFT:MR)= (10/100) = 0.10
P(AFT:HR)= (20/100) = 0.20
The question therefore seeks to determine probability of a high risk diver causing at fault accident, which can be denoted by P(HR:AFT). In line with Bayes’ theory on conditional probability where one can use known conditional probability to find the reverse probability is what can ...
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