standard deviation. Solution: A sample is a subset of a population. A population consists of every member of a particular group of interest. The variance and the standard deviation require that we know whether we have a sample or a population. 2. The following numbers represent the weights in pounds of six 7year old children in Mrs. Jones ’ 2nd grade class. {25‚ 60‚ 51‚ 47‚ 49‚ 45} Find the mean; median; mode; range; quartiles; variance; standard deviation. Solution: mean = 46.166.... median = 48 mode
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1900/4 N=[1.645*(1900/4)/100]^2=62 A sample of 62 is needed. Your sample data has mean 3.1948 and standard deviation 0.0889‚ with a sample size of 25. X (bar) = 3.948‚ s =0.0889‚ n = 25 Use a one-sample t-test Conditions/assumptions for a t-test •Random sample- our survey was a random sample of 25 stations •Normal distribution –we are assuming gasoline prices are normally distributed Null hypothesis: The mean regular unleaded gas prices for your region is the same as that in the
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means using random numbers in scientific computing. More precisely‚ it means using random numbers as a tool to compute something that is not random. For example1 ‚ let X be a random variable and write its expected value as A = E[X]. If we can generate X1 ‚ . . . ‚ Xn ‚ n independent random variables with the same distribution‚ then we can make the approximation A ≈ An = 1 n n Xk . k=1 The strong law of large numbers states that An → A as n → ∞. The Xk and An are random and (depending
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Issuing Debt and Bond Valuation 1. Internally generated funds and stock issuances are available for for-profit and internally generated funds‚ philanthropy‚ government grants‚ and sale of real estate are available to not-for-profit health care providers to increase their equity position. 2. The advantages of a taxpaying entity in issuing debt are fixed debt service payments‚ fixed interest rate‚ no risk ha investor sells bond back‚ and no leer of credit needed‚ while disadvantages are higher
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If x has the probability distribution f(x) = 12x for x = 1‚2‚3‚…‚ show that E(2X) does not exist. This is famous Petersburg paradox‚ according to which a player’s expectation is infinite (does not exist) if he is to receive 2x dollars when‚ in a series of flips of a balanced coin‚ the first head appears on the xth flip. 17. The manager of a bakery knows that the number of chocolate cakes he can sell on any given day is a random variable having the probability distribution f(x) = 16 for x = 0‚1
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Probability Games Walter J Mahoney MTH 157 1/20/2013 Andrea Hayes Probability is a fascinating math concept. It can be applied in many aspects of our students’ daily lives. As the world of technology continues to grow‚ teaching of many math
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Simple random sample (SRS) In statistics‚ a simple random sample from a population is a sample chosen randomly‚ so that each possible sample has the same probability of being chosen. One consequence is that each member of the population has the same probability of being chosen as any other. In small populations such sampling is typically done "without replacement"‚ i.e.‚ one deliberately avoids choosing any member of the population more than once. Although simple random sampling can be conducted
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Chapter 1 The Probability in Everyday Life In This Chapter Recognizing the prevalence and impact of probability in your everyday life Taking different approaches to finding probabilities Steering clear of common probability misconceptions You’ve heard it‚ thought it‚ and said it before: “What are the odds of that happening?” Someone wins the lottery not once‚ but twice. You accidentally run into a friend you haven’t seen since high school during a vacation in Florida. A cop pulls you over the
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Problem 1 Suppose that 6 female and 5 female applicants have been successfully screened for 5 positions. If the 5 positions are filled at random form the 11 finalists‚ what is the probability of selecting: A: 3 females and 2 males? B: 4 females and 1 male? C: 5 females? D: At least 4 females? Problem 2 By examining the past driving records of drivers in a certain city‚ an insurance company has determined the following (empirical) probabilities: [pic] If a driver in this city
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Week Four Discussion 2 1. In your own words‚ describe two main differences between classical and empirical probabilities. The differences between classical and empirical probabilities are that classical assumes that all outcomes are likely to occur‚ while empirical involves actually physically observing and collecting the information. 2. Gather coins you find around your home or in your pocket or purse. You will need an even number of coins (any denomination) between 16 and 30. You do not
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