1. A manufacturer supplies DVD players to retailers in batches of 20. Over the past 12months the manufacturer had 30% of the players returned because they were faulty.(a) Give two reasons why a binomial distribution may be a suitable model for the numberof faulty DVD players in a batch.(b) Find the probability that a random batch of DVD players supplied by thismanufacturer containsno faulty DVD players.more than 4 faulty DVD players.(i)(ii)(c) Find the mean and variance of the number of faulty DVD players in a batch.The company considered this unacceptable and introduced a new quality control strategyaiming to reduce the number of faulty DVD players.One month after the new strategy, a random batch of 20 DVD players was inspected and 4were found faulty.(d) Write down suitable hypotheses and carry out a hypothesis test at the 5 % level todetermine whether there is evidence to suggest that this is correct.2. Two teams, Realers and Senlers, meet for a quiz night. From past results it seems that inyears Realers win, the probability of winning the next year is 0.7 when the Settlers winthe probability of them winning is 0,5. It is not possible for the quiz to end in a druw.The Realers won the quiz in 2016.a. Draw a probability tree diagram for the first three years up to 2019.b. Find the probability that the Settlers will win in 2019.3. A group of 50 students were asked which of three textbooks, Management (M),Quantitative Methods (Q) or English (E) they read daily. The responds showed that 25read M,16 read Q. 14 read E, 5 read both M and Q. 4 read both Q and E, 6 read both Eand M and 2 read all 3.a. Represent these data on a Venn diagram.Find the probability that a student selected at random from this group reads:b. At least I of the textbooks daily.c. Only I of the textbooks.d. Only Management textbooks.

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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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A wholesaler has purchased electronic parts from a supplier for several years and has found that 10% of the parts must be returned because they are defective. An order of 12 parts is received. What is the probability that no more than three of these parts are defective?
Estimate the absolute standard deviation and the coefficient of variation for the results of the following calculations. Round each result to include only significant figures. The numbers in parentheses are absolute standard deviations. y = 1.09(+0.02) x 10-8-3.60(0.2) × 10-⁹ a. Absolute standard deviation = Coefficient of variation - Result = b. y = Absolute standard deviation = Coefficient of variation = Result = % 1.49(0.02) x 10-24.97(10.06) × 10-³ 27.1(0.7)+8.99 (+0.08) %
5. Emergency patients arrive at a dental surgery at a mean rate of one every 2 hours. Calculate the probability that such a patient arrives within the next 1.5 hours. The surgery manager wants to avoid the arrival of two such patients within one half-hour period. Calculate the probability of this event happening.
Researchers are concerned about the rise in gun violence in their community among the adolescent population. Suppose the researchers believe that this rise in violence is due to an increase in depressive symptoms among the demographic aged 11-17. Suppose the researchers estimate that only 21% of this population suffers from depressive-like symptoms. Use a binomial distribution to solve for the following. a) What is the probability of finding no one with depressive-like symptoms in a sample of 8? b) What is the probability that at least 2 respondents of a sample of 8 report these symptoms? c) What is the expected number of adolescents in the sample to report the symptoms?
3. Consider a property market where the price of your apartment is mod- elled by a binomial random variable. Under current market conditions, the probability that the value of your apartment increases in value by 5% (of its original value) in one month is 0.45. The probability that it decreases in value by 5% (of its original value) in one month is 0.55. Given your past experience with lockdowns and apartment living, you decide to relocate to a regional area in 6 months time. Let X denote the number of increases in the price of your apartment over these 6 months. (a) Find E(X) and o(X). (b) Let Y be the random variable which models the percentage change in the price of your apartment. Then Y = 0.05.X-0.05(6-X) because 0.05.X is the total percentage increase in price and 0.05(6- X) is the total percentage decrease in price. Simplify the expres- sion for Y in terms of X. Then using (a), find E(Y) and o(Y).
1. Refer to a 2008 report that states that 35% of US households have at least one high-definition television. Use the approximation to the binomial distribution to calculate the probability that exactly 3 of 16 randomly selected households will have at least one high-definition television
The Washington Wizards and the Philadelphia 76ers are two teams in the National Basketball Association. Washington and Philadelphia will play multiple times over the course of an NBA season. Assume that the Washington has a 25% probability of winning each game against the Philadelphia. Construct a simulation model that uses the negative binomial distribution to simulate the number of games Washington would lose before winning four games against the Philadelphia. Now suppose that the Wizards face the Philadelphia in a best-ofseven playoff series in which the first team to win four games out of seven wins the series. Using the simulation model from part (a), estimate that probability that the Washington would win a best-of-seven series against the Philadelphia 76ers.
1. The distributional pattern of pulmonate slugs inhabiting Libya was studied in the AIUB Journal of Science and Engineering (Aug. 2003). The number of slugs of a certain species found in the survey area was modeled using the negative binomial distribution. Assume that the probability of observing a slug of a certain species (say, Milax rusticus) in the survey area is 0.2. Let Y represent the number of slugs that must be collected in order to obtain a sample of 10 Milax rusticus slugs. a. Give the probability distribution for Y as a formula. b. What is the expected value of Y? Interpret this value.c. Find P(Y = 25).
About 69% of people who are murdered knew the person who committed the murder. Suppose that Detective Williams's case load currently has 49 unsolved murders. Use a nomal distribution approximation to the binomial distribution to find the following probabilities: a. What is the probability that at least 30 of the victims among Detective Williams's case files knew their murderer? b. What is the probability that between 30 and 39 of the victims knew their murderer?
2. Of people who died in the United States in a recent year, 86% were white, 12% were black, and 2% were Asian. (These values ignore a small number of earths among other races. ) Diabetes caused 2.8% of deaths among whites, 4.4% among blacks, and 3.5% among Asians. (a) draw a completely labeled probability tree for this problem. (b) calculate the overall percent of people who died of diabetes across all the three races. (c) given a randomly selected dead person died of diabetes, what is the probability that he/she was white?
I. Boston Children’s Hospital estimates that 90% of Americans have had chickenpoxby the time they reach adulthood.32(a) Suppose we take a random sample of 100 American adults. Is the use of the binomial distributionappropriate for calculating the probability that exactly 97 out of 100 randomly sampled Americanadults had chickenpox during childhood? Explain.(b) Calculate the probability that exactly 97 out of 100 randomly sampled American adults had chickenpoxduring childhood.(c) What is the probability that exactly 3 out of a new sample of 100 American adults have not hadchickenpox in their childhood?(d) What is the probability that at least 1 out of 10 randomly sampled American adults have had chickenpox?(e) What is the probability that at most 3 out of 10 randomly sampled American adults have not hadchickenpox?
If the probability of a machine producing a defective part is 0.01, what is the probability of finding exactly 1 defective part from a sample of 10? (Assume that the process follows a binomial distribution)

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