问题 解答题
有一批货物需要用汽车从生产商所在城市甲运至销售商所在城市乙,已知从城市甲到城市乙只有两条公路,且通过这两条公路所用的时间互不影响。
据调查统计,通过这两条公路从城市甲到城市乙的200辆汽车所用时间的频数分布如下表:
所用的时间(天数)
10
11
12
13
通过公路1的频数
20
40
20
20
通过公路2的频数
10
40
40
10
假设汽车A只能在约定日期(某月某日)的前11天出发,汽车B只能在约定日期的前12天出发。
(1)为了尽最大可能在各自允许的时间内将货物运往城市乙,估计汽车A和汽车B应如何选择各自的路径;
(2)若通过公路1、公路2的“一次性费用”分别为3.2万元、1.6万元(其它费用忽略不计),此项费用由生产商承担。如果生产商恰能在约定日期当天将货物送到,则销售商一次性支付给生产商40万元,若在约定日期前送到,每提前一天销售商将多支付给生产商2万元;若在约定日期后送到,每迟到一天销售商将少支付给生产商2万元。如果汽车A、B长期按(1)所选路径运输货物,试比较哪辆汽车为生产商获得的毛利润更大。
(注:毛利润=(销售商支付给生产商的费用)—(一次性费用))
答案

(1)A选路1,B选路2; (2)B的利润大

题目分析:(I)求出频率分布表,计算汽车A在约定日期(某月某日)的前11天出发选择公路1,2将货物运往城市乙的概率;汽车B在约定日期(某月某日)的前12天出发选择公路1,2将货物运往城市乙的概率,即可得到结论;

(II)分别确定汽车A、B为生产商获得毛利润的概率分布列,求出期望,比较期望值,即可得到结论

解:(I)频率分布表,如下:

所用的时间(天数)10111213
通过公路1的频数0.20.40.20.2
通过公路2的频数0.10.40.40.1
设A1,A2分别表示汽车A在约定日期(某月某日)的前11天出发选择公路1,2将货物运往城市乙;B1,B2分别表示汽车B在约定日期(某月某日)的前12天出发选择公路1,2将货物运往城市乙.

∵P(A1)=0.2+0.4=0.6,P(A2)=0.1+0.4=0.5,∴汽车A选择公路1,

∵P(B1)=0.2+0.4+0.2=0.8,P(B2)=0.1+0.4+0.4=0.9,∴汽车A选择公路2;

(II)设X表示汽车A选择公路1,销售商支付给生产商的费用,则X=42,40,38,36

X的分布列如下:

 X 42 40 3836 
 P 0.2 0.4 0.2 0.2
∴E(X)=42×0.2+40×0.4+38×0.2+36×0.2=39.2

∴汽车A选择公路1时的毛利润为39.2-3.2=36.0(万元)

设Y为汽车B选择公路2时的毛利润,则Y=42.4,40.4,38.4,36.4

分布列如下

 Y 42.4 40.4 38.436.4
 P 0.1 0.4 0.4 0.1
∴E(Y)=42.4×0.1+40.4×0.4+38.4×0.4+36.4×0.1=39.4

∵36.0<39.4,∴汽车B为生产商获得毛利润更大.

点评:本题考查离散型随机变量的分布列和期望,考查比较两个变量的期望值,得到最优思路,是一个利用概率知识解决实际问题的题目,是一个综合题目

阅读理解

阅读理解。

     Imagine a classroom missing the one thing that's long been considered a necessary part to

reading and writing paper.No notebooks,no textbooks,no test paper.Nor are there any pencils

or pens,which always seem to run out of ink at the critical moment.A"paperless classroom"is

what more and more schools are trying to achieve.

     Students don't do any handwriting in this class.Instead,they use palm size,or

specially-designed computers.The teacher downloads texts from Internet libraries and sends

them to every student's personal computer.

     Having computers also means that students can use the Web.They can look up information

on any subject they're studying from maths to social science.

     High school teacher Judy Herrell in Florida,US,described how her class used the Web to

learn about the war in Afganistan(阿富汗) over one year ago.

     "We could touch every side of the country through different sites from the forest to refugee

camps(难民营),"she said."Using a book that's three or four years old is impossible."

     And exams can go online too.At a high school in Tennessee,US,students take tests on

their own computers.The teacher records the grades on the network for everyone to see and

then copies them to his own electronic grade book.

     A paperless classroom is a big step towards reducing the waste of paper.High school

teacher Stephanie Sorrell in Kentucky US said she used to give about 900 pieces of paper

each week to each student.

     "Think about the money and trees we could save with the computers,"she said.But,with

all this technology,there's always the risk that the machines will break_down.So, in case of

a power failure or technical problems, paper textbooks are still widely available(可用的) for

these hitech students.

1.What does the part of the last but one sentence in the first paragraph,"run out of ink at

the critical moment" mean?

A.Pens may not write welt at the critical moment.

B.Pens get lost easily,so you may not find them at the critical moment.

C.Pens may have little or no ink at the critical moment.

D.Pens use ink,while pencils don't.

2.In a paperless classroom, what is a must?

A.Pens.           

B.Computers.  

C.Information.               

D.Texts.

3.The high school teacher,Judy Herrell,used the example of her class to show that________.

A.the Web could take them everywhere

B.the Web taught them a lot

C.the Web is a good tool for information

D.the Web,better than the textbooks,can give the latest and comprehensive(全面的) information

4.The paperless classrooms will benefit ________ the most.

A.students          

B.teachers  

C.trees              

D.computers

5.What does the phrase in the last paragraph,“break down”,mean?

A.Break into pieces.        

B.Stop working.

C.Fall down.              

D.Lose control.

单项选择题