Assignment No. 2 September 23‚ 2014 Case Study: Motion Picture Industry Course: ‐Statistics Professor: Homayoun Khamooshi‚ Ph. D. Team Members: Selena El Hajji Cristina Brain Vizcarra Mandatory Integrity Document for MSPM Team Projects Cristina Brain Vizcarra: “I am satisfied that the contribution made by each team member warrants a full share of the credit for this work‚ and I affirm that I have completed this assignment in accordance with the Code of Academic Integrity
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Quantitative Methods Prof. L. Shridharan PRACTICE PROBLEMS 1. (a) What is the probability that a leap year selected at random will contain 53 Tuesdays? (b) What is the probability that a leap year selected at random will contain 53 Sundays or 53 Mondays? 2. A bag contains 8 black‚ 3 red and 9 white balls. If 3 balls are drawn at random ‚ find the probability that (a) all are black‚ (b) 2 are black and 1 is
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size normally distributed with a mean of 6.0‚ and a standard deviation of 1.0. I am going to order 5000 garnet wedding rings from my reliable Siberian source. They will manufacture ring size from 4.0‚ 4.5‚ 5.0‚ 5.5‚ 6.0‚ 6.5‚ 7.0‚ 7.5‚ 8.0‚ 8.5‚ 9.0‚ and 9.5. How many wedding rings should I order for each of the ring size if I order 5000 rings altogether? (Note: It is natural to assume that if your ring size falls between two of the above standard manufacturing size‚ you will take the bigger of
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distribution with a standard deviation of $40‚000. a. If we select a random sample of 50 households‚ what is the standard error of the mean? b. What is the expected shape of the distribution of the sample mean? c. What is the likelihood of selecting a sample with a mean of at least $112‚000? d. What is the likelihood of selecting a sample with a mean of more than $100‚000? e. Find the likelihood of selecting a sample with a mean of more than $100‚000 but less than $112‚000. a) The standard error of the
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decimals) Q-2b: What is the median amount spent on textbooks? (Round to two decimals) Q-2c: What is the mode with respect to the number of affiliations to clubs and other organizations of these undergraduates? Q-2d: What is the standard deviation of these students’ GPAs? (Round to two decimals) Q-2e: Using coefficients of variation‚ tell me which has more variation‚ the age of the students in this sample or the amounts that they spent on textbooks. ANSWERS Q-2a) The average
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average total of 360 drives per day. The company runs quality checks called PDQ tests on one of their drives every hour of production. The test takes up to 20 minutes. Their historical “in control” process is defined with a mean of 7.0 and a standard deviation of .3. Four-D performs their own PDQ tests on the drives that DataStor ships them. They sample ten drives at random. If any of the drives have a PDQ score of 6.2 or below‚ then the entire shipment will be rejected. Penalties are assessed
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suppose the numbers given are a‚ b‚ c and d‚ where a2*10} Using Chebyshev inequality‚ we note that theta is 50‚ standard deviation is 10‚ and hence 2 is what we called c in the formula. So‚ Pr{X-50>2*10} [pic] . Notice that Chebyshev inequality provides a bound for almost every distribution. It says that if X is picked from the population which has mean θ and standard deviation s‚ the probability that any one realization of x is [pic]farther from θ is less than [pic] . I am using k deliberately
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P is approximated by a normal distribution if Where this applies: Mean = Standard Error = Z-Values for Proportions Using the sample distribution for Proportions Determine the population proportion‚ Calculate the sample proportion‚ p Derive the mean and standard deviation of the sampling distribution Define the event of interest If n and n(1- are both > 5‚ the convert p to z-value Use the standard normal table to determine probability Chapter 8: Estimating Single Population Parameters
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next year the following relationships are possible: Economic Status Probability Rate of Return Weak Economy .15 -5% Static Economy .60 5% Strong Economy .25 15% 9 What is your expected rate of return [E(Ri)] for next year? 10 Compute the standard deviation of the rate of return for the one year period. 11 Compute the coefficient of variation for your portfolio. USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS Assume that during the past year the consumer price index increased by 1.5
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Homework 2 1. Consider a sample with data values of 27‚ 25‚ 20‚ 15‚ 30‚ 34‚ 28‚ and 25. a) Compute the mean‚ median‚ and mode. b) Compute the 20th‚ 65th‚ and 75th percentiles. c) Compute the range‚ interquartile range‚ variance‚ and standard deviation. Answers: Data values: 15‚ 20‚ 25‚ 25‚ 27‚ 28‚ 30‚ 34 a) Mean: [pic]= ∑xi/n = (15+20+25+25+27+28+30+34) / 8 = 204 / 8 = 25.5 Median: Even number‚ so median is = (25+27)/2 = 26 Mode: Most frequent number = 25
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