課程名稱： 統計學
課程性質： 必修
課程範圍： 指數分配、抽樣分配、區間估計......
開課教師： 羅光達
開課學院： 社會科學院
開課系級： 財政系
考試日期(年月日)： 2014.1.13
考試時限(Mins)： 18:30-21:30
附註：
試題本文：
Guidance:
1.Do all questions and write legibly.
2.Total point=100; Suggested=150 minutes.
3.Please keep your original copy of quizzes/midterm/final, in
case you need it to correct your scores.
4.最後答案取至小數點後第二位，但若為查表值需與附表相同。
Question 1 (10%)
Let X have a binomial distribution with parameters n=150 and p=0.6.
Approximate the probability that 82 < x < 101.
Question 2 (10%, 5/5)
假設一棟大樓無預警跳電的相隔天數服從指數分配，且過去的紀錄顯示平均
50天會發生2次跳電。求下列事件發生之機率：
(1) 兩次無預警跳電的間隔時間少於10天。
(2) 兩次無預警跳電的間隔時間多於20天。
Question 3 (10%, 5/5)
A statistical analysis of 1000 long-distance telephone calls made
from the headquarters of the Bricks and Clicks Computer Corporation
indicates that the length of these calls is normally distributed
with μ = 240 seconds and σ = 40 seconds.
(1) What is the probability that a call lasted between 110 and 180
seconds?
(2) What is the length of a particular call if only 2.5% of calls
are shorter?
Question 4 (20%, 10/10)
Let a random variable X have the following probability distribution
x -2 0 2
P(X=x) 0.2 0.6 0.2
_
(1) Obtain the sampling distribution of X for a random sample of 2.
(2) Calculate E(X) and Var(X) for the sampling distribution in (1).
Question 5 (20%)
A survey of 1000 workers were asked how much they used the Internet
at work. 600 said they used it within limits, and 260 said they did
not use the Internet at work.
(1) Construct a 95% confidence interval estimate for the proportion
of all workers who used the Internet within limits.
(2) What sample size was required under 95% confidence interval, if
you want to estimate the population proportion of within a sampling
error of all workers who used the Internet within limits ±0.02 ?
Question 6 (20%, 5/15)
The file contains the amount that a sample of 9 customers spent for lunch
($) at a fast food restaurant
4.20 5.03 5.86 6.45 7.38 7.54 8.46 8.47 9.87
_
(1) Find X and S.
(2) Construct a 95% confidence interval estimate for the population mean
amount spent for lunch($) at a fast food restaurant, assuming a normal
distribution.
Question 7 (10%)
請解釋何謂分層抽樣(Stratified Sampling)及部落抽樣(Clustered Sampling) ?
並各舉一例加以說明。