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東吳大學期末考試題
科目名稱： 商用統計學 時間／節次／份數： 107 年 1 月 18 日 7, 8, 9 節 （51 份）
科目代碼： BIT20603 教師： 賀德崇 系級： 貿二Ａ C 組 題上作答：是 否
班級： 學號： 組別： 姓名：
1）The following table indicates the percentage of residential electricity consumption in the United States, in a recent year organized by type of use.
Construct a Pareto chart. [8分]
2）Construct a stem-and-leaf display, given the following data from a sample of midterm exam scores in finance:
54 69 98 93 53 74 [10分]
3）Consider a population of 1024 mutual funds that primarily invest in large companies. You have determind that μ, the mean one-year total percentage return achieved by all the funds, is 8.20 and that σ, the standard deviation, is 2,75.
(a)According to the empirical rule, what percentage of these funds is expected to be within ±2 standard deviations of the mean? [4分]
(b)According to Chebyshev’s theorem, at least 93.75% of these funds are expected to have one-year total returns between what two amounts? [4分]
4）311 is Chicago’s web and phone portal for government information and nonemergency services. 311 serves as a comprehensive one-stop shop for residents, visitors, and business owners; therefore, it is critical that 311 representatives answer calls and respond to requests in a timely and accurate fashion. The target response time for answering 311 calls is 45 seconds. Agent abandonment rate is one of several call center metrics
tracked by 311 officials. This metric tracks the percentage of callers who hang up after the target response time of 45 seconds has elapsed The file 311CallCenter contains the agent abandonment rate for 22 weeks of call center operation during the 7:00AM-3:00PM, shift.
(a)Compute the mean, median, variance. [3分]
(b)Compute the correlation coefficient between day and agent abandonment rate. [5分]
5）A student is taking a multiple-choice exam in which each question has four choice. Assume that the student has no knowledge of the correct answers to any of the question. She has decided on a strategy in which she will place four balls (marked A, B, C, and D) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question.
There are five multiple-choice question on the exam.
What is the probability that she will get (a)five question correct ? [4分]
(b)no more than two question correct ? [4分]
Type of Use %
Cooking (Ck) 2%
Cooling (Cl) 15%
Electronics (El) 9%
Heating (He) 15%
Lighting (Li) 13%
Refrigeration (Re) 10%
Water heating (WH) 10%
Wet cleaning (WC) 3%
Other (Ot) 23%
Day % Day % 1 10 12 5
2 9 13 9
3 9 14 10
4 6 15 13
5 9 16 17
6 9 17 24
7 14 18 26 8 11 19 21
9 9 20 23
10 10 21 34 11 7 22 20
《背面還有題目》
第 2 頁 共 2 頁 6）Assume a Poisson distribution. (e≒2.71828)
(a) If λ = 2.5 , find P(X = 2). [2分]
(b) If λ = 8.0 , find P(X = 8). [2分]
(c) If λ = 0.5 , find P(X = 1). [2分]
(d) If λ = 3.7, find P(X = 0). [2分]
7）An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.75 inch. The lower and upper specification limits under which the ball bearing s can operate are 0.74 inch and 0.76 inch, respectively. Past experience has indicated that the actual diameter of the ball bearings is approximately normally distributed, with a mean of 0.753 inch and a standard deviation of 0.004 inch.
(a) between the lower specification limit and the target ? [4分]
(b) Of all the ball bearings, 93% of the diameters are greater than what value ? [4分]
8）An orange juice producer buys oranges from a large orange grove that has one variety of orange. The amounts of juice squeezed from these oranges is approximately normally distributed with a mean of 4.7 ounces and a standard deviation of 0.40 ounce.
Suppose that you select a sample of 25 oranges.
(a) what is the probability that the sample mean amount of juice will be at least 4.6 ounces? [4分]
(b) The probability is 70% that the sample mean amount of juice will be contained between what two values symmetrically distributed around the population mean ? [4分]
9）In a survey of 3,187 travelers, 1,465 said that location was very important and 1,181 said that room quality was very important in choosing a hotel.
(a) Construct a 90% confidence interval estimate for the population proportion of travelers who said that location was very important for choosing a hotel.
[4分]
(b) Construct a 90% confidence interval estimate for the population proportion of travelers who said that room quality was very important in choosing a hotel. [4分]
10）An advertising executive wants to estimate the mean weekly amounts of time consumers spend watching television daily. Based on previous studies, the standard deviation is assumed to be 20 minutes.
The executive wants to estimate, with 99%
confidence, the mean weekly amount of time to within ±5 minutes.
(a) What sample size is needed? [4分]
(b) If 95% confidence is desired, how many consumers need to be selected? [4分]
11）假設某廠牌罐裝奶粉每罐平均重量為500克，
變異數為120，現品管人員抽取30罐檢驗其重量，
試問：
(1)抽取之 30 罐的樣本平均重量與母體平均數之
差在3公克之內的機率為何？[3分]
(2)以母體平均數為中心，涵蓋95%的樣本平均數
的區間為何？[3分]
12）製藥廠製造一種抗胃癌新藥，假設每顆藥丸重 量符合常態分配N（0.3 , 0.012），單位：g，因為 此藥含有某成分比率的珍貴藥材與劇毒，製造產 品需要較嚴格的品管。製藥廠認為此抗癌新藥的 重量應為（0.3 ± 0.02）之間才安全。試問，此種 抗癌新藥產品不被接受的比率有多少？
