is the process of selecting from among a group of theoretically possible alternatives of those elements or factors whose combination will most closely approximate a desired result.
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- you sampled 3 components out of an entire population [all of which are unique] of 10. What are the following: If (a) P(Your sample includes the largest of the population) (b) P(Your sample does not include the largest of the population) (c) P(Your sample includes the 2 smallest of the population) (d) P(Your sample includes the 4 largest of the population) (e) P(Your sample includes both the largest and the smallest of the population)Blood is taken from each of n individuals to be tested for a certain disease. Rather than test each sample separately, a pooled method is used in an attempt to reduce the number of tests needed. Part of each blood sample is taken, and these parts are combined to form a pooled sample. The pooled sample is then tested. If the result is negative, then none of the n individuals has the disease, and no further tests are needed. If the pooled sample tests positive, then each individual is tested to see which of them have the disease. a) Let X represent the number of tests that are carried out. What are the possible values of X? b) Assume that n = 4 individuals are to be tested, and the probability that each has the disease, independent of the others, is p = 0.1. Find µX. c) Repeat part (b) with n = 6and p = 0.2. d) Express µX as a function of n and p. e) The pooled method is more economical than performing individual tests if µX < n. Suppose n = 10. For what values of p is the pooled…Suppose that Jeremy is a highschool science teacher and that he is dividing 16 students in his advanced chemistry class into four groups of four for a lab activity. Each of the four lab groups has been assigned its own task to complete for the activity, but the students are not assigned specific roles within the group. How many different ways can Jeremy assign his students to the four lab groups?
- 6) From historical data at a local restaurant indicate that 60% of the customers order coffee, 15% order soft drinks, and the remaining order water. The owner of the restaurant is planning on opening a new restaurant and for purposes of stocking enough of the various drinks, wants to know if the proportions are the same for his new restaurant as they were for his original restaurant. In a sample of 1000 customers at the new restaurant, 550 ordered coffee, 190 ordered soft drinks, and the remaining simply wanted water. At the 5% level of significance, does it appear the proportions have changed?Suppose that 20% of the adult population in Palestine smoke cigarettes only, 15% smoke Argeeleh only, and 10% smoke both cigarettes and Argeeleh. Suppose that 15% of those who smoke cigarettes only have respiratory problems, 10% of those who smoke Agreeleh only have respiratory problems, 20% of those who smoke both cigarettes and Argeeleh have respiratory problems, and 5% of non-smokers have respiratory problems. If an adult person is randomly selected from the population: What is the probability that he/she has respiratory problems? If the selected individual has respiratory problems, what is the probability that he/she is non-smoker? If the selected individual has respiratory problems, what is the probability that he/she smokes both cigarettes and Argeeleh?In a classic study of problem solving, Duncker (1945) asked participants to mount a candle on a wall in an upright position so that it would burn normally. One group was given a candle, a book of matches, and a box of tacks. A second group was given the same items, except that the tacks and the box were presented separately as two distinct items. The solution to this problem involves using the tacks to mount the box on the wall, creating a shelf for the candle. Duncker reasoned that the first group of participants would have trouble seeing a new function for the box (a shelf) because it was already serving a function (holding tacks). For each participant, the amount of time to solve the problem was recorded. Data similar to Duncker’s are as follows. Time to Solve Problem (in sec.) Box of Tacks Tacks and Box Separate 128 42 160…
- A murder scene is found with two types of blood - that of the victim and that ofthe murderer. As luck would have it, the unidentified blood has an incredibly rareblood disorder, only found in 1 in every million men. The capital and surroundingareas have a population of 20 million - and the police are sure the murderer isfrom the capital. The police have already started cataloging all citizens' bloodtypes for their new super crime-database. They already have nearly 1 millionmale samples in there - and bingo - one man, Mr XY, is a match. He is promptlymarched off to trial, there is no other evidence, but the jury are told that the oddsare 1 in a million that he is innocent. He is duly convicted. The question is, howlikely is it that he did not commit this crime?In a survey of 165 students, it was found that 65 students use Facebook, 85 students use Instagram, 50 students use Twitter, 25 students use both Facebook and Instagram, 15 students use both Facebook and Twitter, 20 students use both Twitter and Instagram, 10 students use all three social media platforms (Facebook, Instagram and Twitter). (a) Find the number of students who use exactly one of the three social media platforms. (b) Find the number of students who use none of the three social media platforms.A car insurance company has determined that 9% of all drivers were involved in a car accident last year. Among the 10 drivers living on one particular street, 3 were involved in a car accident last year. If 10 drivers are randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year? O a. O b. O C. O d. 0.4435 0.9548 0.0541 0.0452
