Benford's law states that the probability distribution of the first digits of many items (e.g. populations andexpenses) is not uniform, but has the probabilities shown in this table.Business expenses tend to follow Benford's Law, because there are generally more small expenses than largeexpenses.Perform a "Goodness of Fit" Chi-Squared hypothesis test (a = 0.05) to see if these values are consistent withBenford's Law.If they are not consistent, it there might be embezzelment.Complete this table. The sum of the observed frequencies is 118ObservedX Frequency(Counts)ExpectedFrequency(Counts)Benford'sLaw P(X)137.3012 29.176313.125.0975 5.07966.06710.0588 3.051.046Report all answers accurate to three decimal places.What is the chi-square test-statistic for this data? (Report answer accurate to three decimal places.)What is the P-value for this sample? (Report answer accurate to 3 decimal places.)P-value =The P-value is...O less than (or equal to) aO greater than aThis P-Value leads to a decision to.MacBook ProQ Search or enter website name@#$2&*34678QWEYASFH Report all answers accurate to three decimal places.What is the chi-square test-statistic for this data? (Report answer accurate to three decimal places.)What is the P-value for this sample? (Report answer accurate to 3 decimal places.)P-value =The P-value is...O less than (or equal to) aO greater than aThis P-Value leads to a decision to...O reject the null hypothesisO fail to reject the null hypothesisAs such, the final conclusion is that...There is sufficient evidence to warrant rejection of the claim that these expenses are consistent withBenford's Law..There is not sufficient evidence to warrant rejection of the claim that these expenses are consistentwith Benford's Law..> Next QuestionMacBook ProQ Search or enter website name@#$&*478ETYFGHJKR

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Answered: Benford's law states that the…

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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wendy’s restaurant has been recognized for having the fastest average service time amongfast food restaurants. In a benchmark study, wendy’s average service time of 2.2 minuteswas less than those of Burger King, ChickfilA, Krystal, McDonald’s, Taco Bell, andTaco John’s (QSR Magazine website, December 2014). Assume that the service time forwendy’s has an exponential distribution.a. what is the probability that a service time is less than or equal to one minute?b. what is the probability that a service time is between 30 seconds and one minute?
Data from 14 cities were combined for a 20-year period, and the total 280 city-years included a total of 87 homicides. After finding the mean number of homicides per city-year, find the probability that a randomly selected city-year has the following numbers of homicides, then compare the actual results to those expected by using the Poisson probabilities: Homicides each city-year a. 0 b. 1 C. 2 d. 3 e. 4 Actual results 205 64 10 1 0 a. P(0) = (Round to four decimal places as needed.) b. P(1) = (Round to four decimal places as needed.) c. P(2) = (Round to four decimal places as needed.) d. P(3)= (Round to four decimal places as needed.) e. P(4)= (Round to four decimal places as needed.)
Military radar and missile detection systems are designed to warn a country of an enemy attack. A reliability question is whether a detection system will be able to identify an attack and issue a warning. Assume that a particular detection system has a 0.70 probability of detecting a missile attack. Use the binomial probability distribution to answer the following questions. (a) What is the probability that a single detection system will detect an attack? (b) If two detection systems are installed in the same area and operate independently, what is the probability that at least one of the systems will detect the attack? (c) If three systems are installed, what is the probability that at least one of the systems will detect the attack? (d) Would you recommend that multiple detection systems be used? Explain. Multiple detection systems be used because P(at least 1) for multiple systems very close to 1.
Benford's law states that the probability distribution of the first digits of many items (e.g. populations and expenses) is not uniform, but has the probabilities shown in this table. Business expenses tend to follow Benford's Law, because there are generally more small expenses than large expenses. Perform a "Goodness of Fit" Chi-Squared hypothesis test (a = 0.05) to see if these values are consistent with Benford's Law. If they are not consistent, it there might be embezzelment. Complete this table. The sum of the observed frequencies is 97 Observed Expected Frequency (Counts) Benford's x Frequency (Counts) Law P(X) 1 20 .301 2 27 .176 3 9 .125 4|| 10 .097 5 10 .079 6| 8 .067 73 .058 8 5 .051 95 .046 Report all answers accurate to three decimal places. What is the chi-square test-statistic for this data? (Report answer accurate to three decimal places.) X = What is the P-value for this sample? (Report answer accurate to 3 decimal places.) P-value = The P-value is... O less than (or…
Response team hears directly from consumers about the challenges they face in the marketplace, brings their concerns to the attention of financial institutions, and assists in addressing their complaints. An analysis of complaints registered recently indicates that the mean number of vehicle lease complaints registered by consumers is 3.5 per day. Assume that the number of vehicle lease complaints registered by consumers is distributed as a Poisson random variable. What is the probability that in a given day d. fewer than two vehicle lease complaints will be registered by consumers?
Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was μ = 9.2 mg/L with 95% of the data ranging from 5.4 mg/L to 13.0 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume xhas a probability distribution that is approximately normal. (a) Use the 95% data range to estimate the standard deviation for oxygen demand. (b) An oxygen demand below 8 indicates that some organisms in the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L?(Round your answer to four decimal places.) (c) A high oxygen demand can also indicate trouble. An oxygen demand above 12 may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12…
Assume that the probability of a 25-year-old male living to age 26, based on mortality tables, is 0.993. If a 16,000 dollar one-year term life insurance policy on a 25-year-old male costs 100 dollars, what is its expected value? What is the expected value? The expected value is dollars.
The move to online instruction that was forced on universities by COVID has introducedconsiderable uncertainty in demand for face to face instruction. A business school is trying to decidehow many face to face sections of an introductory accounting course need to be offered in the comingsemester, and has come up with the following probability distribution for demand.Number of students who will choose toattend in person (x) Prob(x)200 .10250 .20300 .40350 .15400 .15a. Is this a valid probability distribution? Why or why not?b. What is the expected value and standard deviation of the number of students who will choose toattend in person?c. Would you say the distribution above obeys the empirical rule? Justify briefly either way.d. Regardless of whether you answered yes or no to (c), assume the empirical rule applies. If youwere the accounting department chair,…
A pharmaceutical company receives large shipments of ibuprofen tablets and uses this acceptance sampling plan: randomly select and test 22 tablets, then accept the whole batch if there is at most one that doesn't meet the required specifications. If a particular shipment of thousands of ibuprofen tablets actually has a 6% rate of defects, what is the probability that this whole shipment will be accepted?Binomial Calculator(Report answer as a decimal value accurate to four decimal places.)P(accept shipment) =
A person with a cough is a persona non grata on airplanes, elevators, or at the theater. In theaters especially, the iitation level rises with each muffled explosion. According to Dr. Brian Carlin, a Pittsburgh pulmonologist, in any large audience you'll hear about 12 coughs per minute. (a) Let r= number of coughs in a given time interval. Explain why the Poisson distribution would be a good choice for the probability distribution of r. O Coughs are a common occurrence. It is reasonable to assume the events are dependent. O Coughs are a common occurrence. It is reasonable to assume the events are independent. O Coughs are a rare occurrence. It is reasonable to assume the events are independent. O Coughs are a rare occurrence. It is reasonable to assume the events are dependent. (b) Find the probability of eleven or fewer coughs (in a large auditorium) in a 1-minute period. (Use 4 decimal places.) (c) Find the probability of at least seven coughs (in a large auditorium) in a 20-second…
Gubser Welding, Inc., operates a welding service for construction and automotive repair jobs. Assume that the arrival of jobs at the company's office can be described by a Poisson probability distribution with an arrival rate of two jobs per 8-hour day. The time required to complete the jobs follows a normal probability distribution, with a mean time of 3.2 hours and a standard deviation of 2.3 hours. Answer the following questions, assuming that Gubser uses one welder to complete all jobs. (a) What is the mean arrival rate in jobs per hour? (Round your answer to four decimal places.) per hour (b) What is the mean service rate in jobs per hour? (Round your answer to four decimal places.) per hour (c) What is the average number of jobs waiting for service? (Round your answer to four decimal places.) (d) What is the average time (in hours) a job waits before the welder can begin working on it? (Round your answer to two decimal places.) h (e) What is the average number of hours between…

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