1.answer at least 2 questions from the list that is listed below. Please be specific with your explanation and if needed use formulas and/or examples to demonstrate your clear understanding of the contents.
Question 1: What are the main categories into which we can classify data values in Statistics?
Question 2: What is the main difference between qualitative and quantitative data? Please support your answer with an example!
Question 3: What are the main measures of Central Tendency in Statistics? Please explain each in detail!
Question 4: Describe a continuous variable and a discrete variable by using an example to support your answers.
Question 5: What are the main applications of a: Histogram, an Ogive, and Stem and Leaf. Please explain in detail!
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2.Suppose that a class contains 20 boys and 30 girls, and that 15 students are to be selected at random for a special assignment. Find the probability that exactly 5 boys will be selected.
3.
Discrete Probability Distributions
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Consider selecting at random a student who is among the 15,000 registered for the current semester at a school.
Let X be the number of courses for which the selected student is registered and suppose that X has probability distribution
x: 1 2 3 4 5 6
P(x): 0.01 0.03 0.13 0.25 0.39 0.19
Find the cdf of X.
Find the expected number of courses taken by a student in this semester.
Find the standard deviation of X.
Find the median of this distribution.
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4.
Using the Normal Distribution
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Suppose the demand for a company’s product in weeks 1, 2, and 3 are each normally distributed and the mean demand during each of these three weeks is 50, 45, and 65, respectively. Suppose the standard deviation of the demand during each of these three weeks is known to be 10, 5, and 15, respectively. It turns out that if we can assume that these three demands are probabilistically independent then the total demand for the three week period is also normally distributed. And, the mean demand for the entire three week period is the sum of the individual means. Likewise, the variance of the demand for the entire three week period is the sum of the individual weekly variances. But be careful! The standard deviation of the demand for the entire 3 week period is not the sum of the individual standard deviations. Square roots don’t work that way!
Now, suppose that the company currently has 180 units in stock, and it will not be receiving any further shipments from its supplier for at least 3 weeks. What is the probability that the company will run out of units?
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5.
Build a Confidence Interval Estimate
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Political polls typically sample randomly from the U.S population to investigate the percentage of voters who favor some candidate or issue. The number of people polled is usually on the order of 1000. Suppose that one such poll asks voters how they feel about the President’s handling of the crisis in the financial markets. The results show that 575 out of the 1280 people polled say they either “approve” or “strongly approve” of the President’s handling of this matter. Based on the sample referenced above, find a 95% confidence interval estimate for the proportion of the entire voter population who “approve” or “strongly approve” of the President’s handling of the crisis in the financial markets.
Now, here’s an interesting twist. If the same sample proportion was found in a sample twice as large—that is, 1150 out of 2560—how would this affect the confidence interval?
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