[試題] 1021 丁兆平 統計學 第一次小考
課程名稱： 統計學
課程性質： 整開
課程範圍： Chapter 1 - Chapter 5
開課教師： 丁兆平
開課學院： 商學院
開課系級： 統計系
考試日期(年月日)： 2013/10/24
考試時限(Mins)： 60 min
附註：
試題本文：
1. Gold Fin is a very popular restaurant located near the National Chengchi University. They serve a variety of Japanese food. During the meal time, they do not take reservations or accept "call ahead" seating. Management of the restaurant is concerned with the time a patron must wait before being seated for dinner. Listed below is the waiting time, in minutes, for the 24 tables seated last Friday night.
28 39 23 67 37 28 56 41 28 49 51 45
44 65 61 27 24 34 44 64 25 24 27 29
a. Determine the level of measurement for this variable. (5 pts)
b. Find the mean, median, and the standard deviation of the data. (10 pts)
c. Organize the data into a frequency table starting with 20. How many classes would you recommend and what class interval would you suggest? (10 pts)
d. Convert the frequency distribution into a frequency polygon. (5 pts)
e. Find the mean and the standard deviation of the data organized into a frequency distribution as in (c). Compare these values with those computed in (b). Why are they different? (10 pts)
f. Develop a box plot of the data and comment on the result. Are there any outliers? (15 pts)
2. If you earn $22,000 a year this year, and you will need to make $28,000 in 5 years to have the same buying power. Assuming that the inflation rate is fixed, what would be the inflation rate per year? (10 pts)
3. A student is taking two course, statistics and economics,this semester. The probability the student will pass the statistics course is 0.60, the probability of passing the economics course is 0.70, and the probability of passing both is 0.50.
a. What is the probability that the student will past at least one course? What is the probability that the student will fail both course? (10 pts)
b. Are the two events mutually exclusive? Explain. (5 pts)
4. Researchers have developed statistical models based on financial ratios that predict if a company will go bankrupt over the next year. In a teset of one such model, the model correctly predict the bankruptcy of 85% of the firms that did in fact fail, and it correctly predicted non-bankruptcy for 74% of firms that did not fail. Suppose that we expect 8% of the firms in a particular city to fail over the next year. Suppose that the model predicts bankruptcy for a firm that you own. What is the
probability that your firm will fail within the next 12 months? (10 pts)
5. In a class on probability, a statistics professor flips two biased coins with heads appearing twice as much as tails. Both fall to the floor and roll under her desk. A student in the first row informs the professor that he can see both coins. He reports that at least one of them shows tails. What is the porbability that the other coin is also tails? (10 pts)
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※ 編輯: Inosxz 來自: 140.119.193.69 (01/16 18:07)