问题 解答题
广东省汕头市日前提出,要提升市民素质和城市文明程度,促进经济发展有大的提速,努力实现“幸福汕头”的共建共享.现随机抽取50位市民,对他们的幸福指数进行统计分析,得到如下分布表:
幸福级别非常幸福幸福不知道不幸福
幸福指数(分)9060300
人数(个)192173
(I)求这50位市民幸福指数的数学期望(即平均值);
(11)以这50人为样本的幸福指数来估计全市市民的总体幸福指数,若从全市市民(人数很多)任选3人,记ξ表示抽到幸福级别为“非常幸福或幸福”市民人数.求ξ的分布列;
(III)从这50位市民中,先随机选一个人.记他的幸福指数为m,然后再随机选另一个人,记他的幸福指数为n,求n<m+60的概率P.
答案

(Ⅰ)记Ex表示这50位市民幸福指数的数学期望,

Ex=

1
50
(90×19+60×21+30×7+0×3)=63.…(1分)

(Ⅱ)ξ的可能取值为0、1、2、3    …(2分)

P(ξ=0)=

C03
(
4
5
)0(
1
5
)3=
1
125
…(3分)

P(ξ=1)=

C13
(
4
5
)1(
1
5
)2=
12
125
…(4分)

P(ξ=2)=

C23
(
4
5
)2(
1
5
)1=
48
125
…(5分)

P(ξ=3)=

C33
(
4
5
)3(
1
5
)0=
64
125
…(6分)

∴ξ分布列为

ξ0123
P
1
125
12
125
48
125
64
125
…(7分)

(Ⅲ)方法一:设所有满足条件的对立事件n≥m+60的概率为P1

①满足m=0且n=60的事件数为:

A13
A121
=63…(8分)

②满足m=0且n=90的事件数为:

A13
A119
=57…(9分)

③满足m=30且n=90的事件数为:

A17
A119
=133…(10分)

P1=

63+57+133
A250
=
253
2450
…(11分)

所以满足条件n<m+60的事件的概率为P=1-P1=1-

253
2450
=
2197
2450
.…(12分)

方法二:基本事件的总数为

A250
=2450

满足条件n<m+60的有如下各种情况:

①满足m=0时,n=0,30的事件数为:

A13
A19
…(8分)

②满足m=30时,n=0,30,60的事件数为:

A17
A130
…(9分)

③满足m=60时,n=0,30,60,90的事件数为:

A121
A149
…(10分)

④满足m=90时,n=0,30,60,90的事件数为:

A119
A149
…(11分)

所以P=

A13
A19
+
A17
A130
+
A121
A149
+
A119
A 49
A250
=
3×9+7×30+21×49+19×49
50×49
=
2197
2450
…(12分)

阅读理解

阅读理解。

      

     People and air pollution are often in the same places. This means that cities with large populations have

  the biggest problem of dirty air. Air pollution is caused by many different things. A major kind of air

 pollution is the gas from cars. Statistics (统计资料) show that 93 percent of all auto trips are within cities.

 Another major kind of dirty air is the burning of coal and oil for energy. This energy is needed to make

 electricity. Of course, much more electricity is used in the city than in the country.

     On the average, we throw away more rubbish than the year before. The burning of rubbish makes air

 pollution even worse. Many major industries are also responsible for the dirty air in the around cities. The

 fumes (烟) from iron, steel, chemical, and petrol production add particles (微粒)  to the air.

     The effects of air pollution range from mild headaches to death. The levels of pollution found in heavy

 traffic may cause headaches for loss of clear vision. Wherever coal and oil are used for fuel, fumes may

  kill trees and plants and cause metal to corrode (腐蚀). In some of the larger cities, these fumes endanger

 the live of human beings by contributing to lung diseases and causing early death.

1. Why is air pollution more in the city than in the country?

    A. Because there are larger populations in cities.

    B. Because the air in the city is dirty.

    C. Because there are more cars in the city.

    D. Because there are much more gas fumes from cars.

2. The fumes from coal and oil may cause metal _____.

    A. to turn black                                      

    B. to become rusty

    C. to corrode                                          

    D. to twist

4. In larger cities,  the fumes from coal and oil may cause _____.

    A. heart diseases                        

    B. lung diseases

    C. loss of clear vision                    

    D. serious headaches

5. The main idea of the passage is that _____.

    A. the cause of air pollution is people

    B. the causes and the effects of air pollution are both found in cities

    C. the effects of air pollution range from headaches to death

    D. air pollution is caused by dirty air

6. What is the purpose of this passage?

    A. To tell people to stop polluting the air.

    B. To tell the causes of air pollution.

    C. To tell why cities are bad places to live in.

    D. To describe why cities are good places to live in.

问答题 简答题