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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Data can be approximated quite well by a N(3.4, 3.1) model. Economists become alarmed when productivity decreases. According to the normal model what is the probability that the percent change in worker output per hour from the previous quarter is more than 1.6 standard deviations below the mean? What is the probability that the percent change in worker output from the previous quarter is between -1.56 and 4.33?
Please use excel formulas when possible: You have a device that uses a single battery, and you operate this device continuously, never turning it off. Whenever a battery fails, you replace it with a brand new one immediately. Suppose the lifetime of a typical batteryhas an exponential distribution with mean 205 minutes. Suppose you operate the device continuously for three days, making battery changes when necessary. Find the probability that you will observe at least 25 failures. (Hint: The number of failures is Poisson distributed.) In the previous problem, we ran the experiment for a certain number of days and then asked about the number of failures. In this problem, we take a different point of view. Suppose you operate the device, starting with a new battery, until you have observed 25 battery failures. What is the probability that at least 15 of these 25 batteries lived at least 3.5 hours? (Hint: Each lifetime is exponentially distributed
A Scenario: Jimmy store sells large tins of Tom Tucker Coffee. The deli uses a periodic review system. Inventory is checked every 10 days which more orders are needed for tins. Order lead time is 3 days. Average demand is 7 tins, so average demand during the reorder period and order lead time (13) is 91 tins. Standard deviation of demand during the same 13 day period is 17 tins.1. Calculate the restocking level ( Assume the desired level is 90%)2. Suppose standard deviation of demand during the 13-day period drops to 4 tins. What happened to restocking level? Explain why?3. Draw a saw-tooth diagram. Beginning inventory level is equal to restocking level and the demand rate is a constant 7 tins per day. What is the safety stock level? What is the average inventory level?
Andrew plans to retire in 40 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that over the entire 20th century, the real (that is, adjusted for inflation) annual returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal. What is the probability (assuming that past pattern of variation continues) that the mean annual return on common stocks over the next 40 years will exceed 10%? What is the probability that the mean return will be less than 5%?
Exercise 6. Regression Fallacy. Historically, scores on the two midterms had a correlation of 0.48. Suppose that Jeri scored 2.1 standard deviations below the mean on the first midterm. (a) How many standard deviations [above or below?] the mean would you predict for her second midterm?
The working life time, in years, of a particular model of electric oven is exponentially distributed with mean of 8. Find the 22th percentile of the working lifetime, in years.
The inflation adjusted annual return of a diversified asset portfolio is assumed to have a normal distribution with a mean of 3.5% and a standard deviation of 1.25%. Represent the value for the inflation adjusted annual return that 95% of outcomes would exceed on a diagram and determine this value.
In a recent year, grade 6 Ohio State public school students taking a mathematics assessment test had a mean score of 303.1 with a standard deviation of 36. Possible test scores could range from 0 to 1000. Assume that the scores were normally distributed. This is not a normal approximation, so do not correct for continuity. Find the probability that a student had a score higher than 295. Find the probability that a student had a score between 230 and 305. What is the highest score that would still place a student in the bottom 16% of the scores? If 4000 students are randomly selected, how many will have a test score that is less than 300? A random sample of 40 students is drawn from this population. What is the probability that the mean test score is greater than 290?
Deandre is in his first semester at a certain university and is taking a calculus course with a large enrollment. He just took the first midterm exam and is nervous about his score. Among all of the students in the course, the mean of the exam was 67 with a standard deviation of 3. Deandre scored a 62 on this exam. (a) Find the z-score of Deandre's exam score relative to the exam scores among all the students in the course. Round your answer to two decimal places. z=0 (b) Fill in the blanks to interpret the z-score of Deandre's exam score. Make sure to express your answer in terms of a positive number of standard deviations. Deandre's exam score was standard deviations (Choose one) ▼ the mean exam score among all students in the course. Calendar ... 80 F3 F4 F6 F7 F8 F9 F10 F11 云