2. An exam in Microeconomics has 40 multiple answer questions and each of them has 4 pos- sible answers, but only one of them is correct. For every correctly answered question a student gets 15 points and for every incorrectly answered she loses 5 points. What is the probability of passing the exam (the minimum required is 120 points) if a student is ran- domly picking the answers? (hint: you may use a normal approximation)

2. An exam in Microeconomics has 40 multiple answer questions and each of them has 4 pos- sible answers, but only one of them is correct. For every correctly answered question a student gets 15 points and for every incorrectly answered she loses 5 points. What is the probability of passing the exam (the minimum required is 120 points) if a student is ran- domly picking the answers? (hint: you may use a normal approximation)

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Description: 2. An exam in Microeconomics has 40 multiple answer questions and each of them has 4 pos-sible answers, but only one of them is correct. For every correctly answered question astudent gets 15 points and for every incorrectly answered she loses 5 poi

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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An exam in Microeconomics has 40 multiple answer questions and each of them has 4 possible answers, but only one of them is correct. For every correctly answered question a student gets 15 points and for every incorrectly answered she loses 5 points. What is the probability of passing the exam (the minimum required is 120 points) if a student is randomly picking the answers? (hint: you may use a normal approximation)
Texas Instruments produces computer chips in production runs of 1 million at a time. It has found that the fraction of defective modules can be very different in different production runs. These differences are caused by small variations in the set-up of each production run. Managers have observed that defective rates are roughly triangular, with a lower bound of 0%, and an upper bound of 50%. Defects more likely to be near 10% than any other single value in their range. Now suppose that we have taken a sample of 10 modules, and 2 of them are defective. i. What is the conditional probability of a defective rate less than 25% in this production run?ii. For what number M would you say that the defective rate is equally likely to be above or below M?
2. A leading researcher in the study of interstate highway accidents proposes that a major cause of many collisions on the interstates is not the speed of the vehicles but rather the difference in speeds of the vehicles. When some vehicles are traveling slowly while other vehicles are traveling at speeds greatly in excess of the speed limit, the faster-moving vehicles may have to change lanes quickly, which can increase the chance of an accident. Thus, when there is a large variation in the speeds of the vehicles in a given location on the interstate, there may be a larger number of accidents than when the traffic is moving at a more uniform speed. The researcher believes that when the standard deviation in speed of vehicles exceeds 10 mph, the rate of accidents is greatly increased. During a 1-hour period of time, a random sample of 50 vehicles is selected from a section of an interstate known to have a high rate of accidents, and their speeds are recorded using a radar gun. The data…
Assume that out of a population of 1871 people, 30% of the population hasa particular genetic characteristic.a. Find the most likely number of the 1871 people to have thegenetic characteristic. Don’t forget to show your work.b.Let ? represent the number of people out of the 1871 whohave the genetic characteristic. Find the standard deviation for theprobability distribution of ?. Don’t forget to show your work.c. Use the range rule of thumb to find the minimum andmaximum usual value. Don’t forget to show your work. Round youranswers to the nearest whole numbers
2. Consider a study where students are measured on whether they had an internship during their time at WKU (Y/N) and whether they had a job at graduation (Y/N). If we wanted to test whether having an internship was associated with having a job at graduation (i.e., internship holders were more likely to have jobs), why would the chi-square test be inappropriate for this hypothesis? How should we analyze our data?
Suppose we take a sample of 2,500 blood donors from a population for which 50% (0.5) have type O+ blood. (a) Into what range of possible values should the sample proportion fall 95% of the time, according to the Empirical Rule? to (b) If the sample included only 625 donors instead of 2,500, would the range of possible sample proportions be wider, more narrow, or the same as with a sample of 2,500 donors? Explain your answer, and explain why it makes intuitive sense. The range would be with 625 donors compared to a sample of 2,500 donors since the standard deviation of the sampling distribution would be . This makes intuitive sense because if fewer donors are included in the sample, the proportion will be reliable as an estimate of the proportion.
An elephant eats an average of 3 bushels of alfalfa per day, with a standarddeviation of 0.8 bushels. Suppose that you need to feed 10 elephants for oneweek. If the distribution is normal, what is the minimum number of bushels ofalfalfa so that there is no more than a 10% chance of running out by the end of the week?
a) Genenesis Dispensary is contemplating of opening a new branch in Mwanza. If the medical for medical service is favourable, Genesis could realize a net profit of Tsh.100 million. On the other hand, if the market turn out to be unfavourable, it can end up losing Tsh. 40 million. Of course, Genesis may opt not to persue this option of expanding its operations. In the absence of data from which to base its decision, te best guess for Gensis is equally likely that the dispensary will either be successful or unsuccessful Required: i) Use the decison tree approach, what decison should Genesis Dispensary take b) Market research firm named, Easy Market Access approach Genesis with an offer to undertake a study of Mwanza medical service market at a fee of Tsh. 5 million. Easy Market Access claims that their experience enables them to use Bayes’ Theoremn to make the following statements about different state of the market: ▪ Provide that the study is favourable, the probability of favourable…
Suppose an electric-vehicle manufacturing company estimates that a driver who commutes 50 miles per day in a particular vehicle has a recharging time that has a uniformly distributed between 70 and 110 minutes. What is the expected recharging time in minutes?(Enter your answer with no decimal places).
When a least squares line is fit to the 12 observations in the labor cost data, we obtain SSE =656, 214.3589. Calculate s2 and s (isnt n-k-1)?
A newspaper article reported that people spends a mean of 6 hours per day watching tv, with a standard deviation of 1.8 hours. A psychologist would like to conduct interviews with the 15% of the population who spend the most time watching tv. She assumes that the daily time spent watching tv is normally distributed. At least how many hours of daily tv watching are necessary to be eligible for the interview? Carry intermediate computations to 4 places, and the answer to 1.
A researcher is using a two-tailed hypothesis test with α = 0.05 to evaluate the effect of a treatment. If the boundaries for the critical region are t = ± 2.080, then how many individuals are in the sample?