Homework answers / question archive / 1) To study the relationship between smoking and lung cancer, from a population, we collect a sample of those who state they have been smoking for years and another sample of those who state they do not smoke

1) To study the relationship between smoking and lung cancer, from a population, we collect a sample of those who state they have been smoking for years and another sample of those who state they do not smoke

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1) To study the relationship between smoking and lung cancer, from a population, we collect a sample of those who state they have been smoking for years and another sample of those who state they do not smoke. Then, we use the observed values as they are, conduct a statistical analysis, and make an appropriate comparison between the two groups for the purpose of investigating the correlation between the smoking and lung cancer.

2) The weight of a bag of chips of a certain brand sold in vending machines is normally distributed with a mean of 16 ounce and a standard deviation of 0.3 ounce. If a customer buys two bags of chips, what is the probability that weights of both of them exceed 16.5 ounce? A fisherman knows by experience the average weight and the standard deviation of a catfish are 3.1 pounds and 0.8 pounds, respectively. Assuming the distribution of catfish is normally distributed, what is the probability that the weight of a randomly caught catfish is not more than 4 pounds?

3) Suppose we are to play an electronic game using a rectangular tablet of size 10 inches by 15 inches. A rectangular target of size 1 inch by 5 inches is marked on the screen. The idea is to land a random moving mouse in the marked area. What is the probability of this event? Here is the solution to the problem: The areas of the screen and the marked area are 10 ⋅ = 15 150 inches2 and 1⋅ = 5 5inches2, respectively. Thus, the probability of hitting the target, that is, be within the marked area, is 5/150 = 0.033, or a very small chance of 3.3%.

4) We may want to choose a digit at random from 3 to 9. Thus, the outcomes may be the digits 3, 4, 5, 6, 7, 8, or 9 that have the same chance of 1/7 to be selected. In other words, all elementary events in {3 , } {4},..., { 9} are equiprobable. Suppose for the purpose of quality control of a product in a manufactory a sample size of 50 is chosen. Items in the sample are checked one at a time for matching the set criteria. Four items failed the match. Thus, the relative frequency of nonmatched items is 4/50, or 8%. We should note the word “approximated” used in the definition above. That is, the probability in this case is “estimated by the portion or proportion”. Thus, no matter how many repetitions of a trial are performed, the exact value of P(E) is not known. Since the repetition of trials and stop at a point are equivalent to sampling in statistics (and simulation, in general), we will discuss finding this error when this subject comes up later.

5) In contrast to the discrete sample space discussed in Example 2.1, we may have continuous sample space. For example, consider a machine that may break while working. The length of breakdown of the machine is an interval of time on the real line, as the length of the working time of the machine. Suppose we are interested in the first time that the machine breaks down. Thus, the sample space for working time of the machine in this case is indicated by [0,∞), where the symbol ∞ denotes that the machine will never break.

6) An executive lady has four clean skirts and five clean blouses to wear to work in a certain week. How many ways can she choose outfits for Monday, Wednesday, and Friday if. i) She does not wish to wear the same skirt or blouse twice? ii) She is willing to repeat her attire? iii. She is willing to repeat her skirts but not her blouses? Suppose stocks of eight electronic items and five real estate buildings are available in the stock market. We want to create a stock shares portfolio with four electronic items and three real estate pieces. How many different ways can we form this portfolio?