Which of the following statements is true? o Rolling a fair die 6,000 times probably results in a proportion of l's closer to 1/6 than if you rolled die 60 times. o If you roll a fair die 6000 times, you will observe a 1 exactly 1000 times. o If you observe a 1 on eight out of ten rolls of a fair die, you are more likely to observe a 1 than a 6 on the next roll. o The die cannot actually be fair if you observe a 1 on each of ten rolls of a die.
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- A television network earns an average of $65 million each season from a hit program and loses an average of $25 million each season on a program that turns out to be a flop. Of all programs picked up by this network in recent years, 30% turn out to be hits; the rest turn out to be flops. At a cost of C dollars, a market research firm will analyze a pilot episode of a prospective program and issue a report predicting whether the given program will end up being a hit. If the program is actually going to be a hit, there is a 65% chance that the market researchers will predict the program to be a hit. If the program is actually going to be a flop, there is only a 40% chance that the market researchers will predict the program to be a hit.Suppose that the link speed is 8 Mbps, the demand bandwidth of each active user is 1000Kbps. The active probability of each user is 10%. How much user can support under the block probability is less than 0.008?In a manufacturing process, there are an average of 10 defects per 100 m2 on a piece. a) Find the probability that there are more than 2 defects on a randomly picked item measuring 5mx5m. b) If 3 pieces of 5mx10m dimensions are chosen randomly, find the probability that only 1 of them has a maximum of 1 defect.
- A professional employee in a large corporation receives an average of 40.0 e-mails per day. Most of these e-mails are from other employees in the company. Because of the large number of e-mails, employees find themselves distracted and are unable to concentrate when they return to their tasks. In an effort to reduce distraction caused by such interruptions, one company established a priority list that all employees were to use before sending an e-mail. One month after the new priority list was put into place, a random sample of 49 employees showed that they were receiving an average of X(bar)= 30.4 e-mails per day. The computer server through which the e-mails are routed showed that s.d.= 16.5 . Use a 5% level of significance to test the claim that there has been a change (either way) in the average number of e-mails received per day per employee. What is the value of the test statistic? Round your answer to three decimal places.A soda company sells one of its soft drinks in 12 ounce cans. In order to ensure that every can has at least 12 ounces in it, the machines in the factory are set to fill each can with an average of 12.1 ounces of soda. Every week, a quality-control technician tests 10 cans to make sure that the average amount of soda in the cans is still 12.1 ounces. If the conclusion of the test is that the number of ounces of soda in the cans is different from 12.1, the technician will declare that the process is out of control, and the machine will be stopped and calibrated. From previous tests, the technician found that the standard deviation of the number of ounces of soda in the cans is approximately 0.01. The number of ounces of soda in the 10 cans that were tested this week is given below. Assume that the standard deviation from the technician's previous tests is the population standard deviation. Use a TI-83, TI-83 Plus, or TI-84 calculator to test whether filling process is out of control and…The KLM Christmas tree Farm owns a plot of land with 5000 evergreen trees.Each year KLM allows retailers of Christmas trees to select and cut trees for sale to individualcustomers. KLM protects small trees (usually less than 4 feet tall) so that they will be availablefor sale in future years. Currently, 1500 trees are classified as protected trees, while theremaining 3500 are available for cutting. However, even though a tree is available for cuttingin a given year, it may not be selected for cutting until future years. Most trees not cut in agiven year live until the next year, but some diseased trees are lost every year. In viewing the KLM Christmas tree operation as a Markov process with yearly periods, we define thefollowing four states:
- A professional employee in a large corporation receives an average of μ = 41.3 e-mails perday. Most of these e-mails are from other employees in the company. Because of the largenumber of e-mails, employees find themselves distracted and are unable to concentrate whenthey return to their tasks. In an effort to reduce distractions caused by such interruptions, onecompany established a priority list that all employees were to use before sending an e-mail.One month after the new priority list was put into place, a random sample of 37 employeesshowed that they were receiving an average of = 34 e-mails per day. The computer serverthrough which the e-mails are routed showed that σ = 16.2. Has the new policy had anyeffect? Use a 5% level of significance to test the claim that there has been a change (eitherway) in the average number of e-mails received per day per employee. What is the value ofthe test statistic? Group of answer choices –0.451 0.074 –0.074 –2.741 2.741A direct sale company started out with two members in the first generation. It is the policy of the company that each member has to recruit another two new members under him or her. Assuming that every member fulfils this condition, find the minimum number of generations such that the total number of members exceeds 1200.A professional employee in a large corporation receives an average of μ = 39.9 e-mails perday. Most of these e-mails are from other employees in the company. Because of the largenumber of e-mails, employees find themselves distracted and are unable to concentrate whenthey return to their tasks. In an effort to reduce distractions caused by such interruptions, onecompany established a priority list that all employees were to use before sending an e-mail.One month after the new priority list was put into place, a random sample of 45 employeesshowed that they were receiving an average of = 33.6 e-mails per day. The computerserver through which the e-mails are routed showed that σ = 17.3. Has the new policy hadany effect? Use a 5% level of significance to test the claim that there has been a change(either way) in the average number of e-mails received per day per employee. Find (orestimate) the P-value. Group of answer choices 0.996 0.015 0.004 0.993 0.985
- When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 36% of the eggs are yellow, and the rest green. Next spring the lead scientist has permission to randomly select 56 of the dragon eggs to incubate. Consider all the possible samples of 56 dragon eggs. find the minimum and the maximum usual number of yellow eggs.At a science fair, 4 different groups of students from a local school are showcasing their projects. The groups arrive with their advisors and each group has a different number of students (40, 33, 25, and 50, respectively). A participant is chosen randomly from the entire pool of students. Let’s use the variable X to represent the number of students in the group that the selected participant belongs to. Meanwhile, the event organizers decide to acknowledge the hard work of one of the advisors by ”randomly selecting” one of them for special recognition. Let’s use the variable Y to represent the number of students who came with the chosen advisor. (a) Before doing any computations, which of E(X) or E(Y) do you think is larger? Or are they the same? Why? (b) Compute E(X) and E(Y). Comment.A private pilot wishes to insure his airplane for $200,000. The insurance company estimates that atotal loss will occur with probability 0.002, a 50% loss with probability 0.01, and a 25% loss withprobability 0.1. Ignoring all other partial losses, what premium should the insurance company chargeeach year to realize an average profit of $500?