题干

某校高三4班有50名学生进行了一场投篮测试,其中男生30人,女生20人.为了了解其投篮成绩,甲、乙两人分别都对全班的学生进行编号(1﹣50号),并以不同的方法进行数据抽样,其中一人用的是系统抽样,另一人用的是分层抽样.若此次投篮测试的成绩大于或等于80分视为优秀,小于80分视为不优秀,如表是甲、乙两人分别抽取的样本数据:
甲抽取的样本数据

编号

2

7

12

17

22

27

32

37

42

47

性别

投篮成 绩

90

60

75

80

83

85

75

80

70

60

乙抽取的样本数据

编号

1

8

10

20

23

28

33

35

43

48

性别

投篮成 绩

95

85

85

70

70

80

60

65

70

60

(Ⅰ)在乙抽取的样本中任取3人,记投篮优秀的学生人数为X,求X的分布列和数学期望.
(Ⅱ)请你根据乙抽取的样本数据完成下列2×2列联表,判断是否有95%以上的把握认为投篮成绩和性别有关?

优秀

非优秀

合计

合计

10

(Ⅲ)判断甲、乙各用何种抽样方法,并根据(Ⅱ)的结论判断哪种抽样方法更优?说明理由.
下面的临界值表供参考:

P(K2≥k)

0.15

0.10

0.05

0.010

0.005

0.001

k

2.072

2.706

3.841

6.635

7.879

10.828

(参考公式:K2=
n
(
a
d
b
c
)
2
(
a
+
b
)
(
c
+
d
)
(
a
+
c
)
(
b
+
d
)
,其中n=a+b+c+d)
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答案(点此获取答案解析)

解:(Ⅰ)在乙抽取的10个样本中,投篮优秀的学生人数为4,

∴X的取值为0,1,2,3. P(x=k)=C4k

同类题3

阅读下面短文, 从短文后各题所给的四个选项(A、B、C、D)中, 选出可以填入空白处的最佳选项。

    It was a beautiful, sunny day. I had just finished1my daughter to the airport to catch an early morning flight. My sons and I2went to a fast-food place for3before heading back home. After eating, we all got into the car and pulled out of the 4. The restaurant was at the very top of a hill. At the bottom of the hill was a5sign, so we found ourselves at the end of a6line of traffic waiting while the cars at the bottom turned onto the7road one at a time.

    As I looked down to the bottom of the hill, my eyes saw an elderly man standing8the stop sign. His clothes were9and shabby (破旧的). He held a cardboard sign with the words “10Help Please!” written on it. My heart went out to him and I11myself in his situation. As car after car turned onto the main road without12for him, I reached for my wallet to look for whatever13was left in it. As I was pulling it out of my wallet,14, I saw a young woman walk up to him along the side of the road. She was carrying a bag full of 15 taken out from the restaurant I was just at. I watched as the old man16the young girl and smiled as she reached out her arms to give him a hug.

    Suddenly a17honk (喇叭声) from the car behind me made me realize that I hadn't been18forward because this simple choice for19had captured (attracted) my attention and my heart. By the time I reached the20of the hill, both the man and the lady who had helped him were gone. Yet, as I drove home, the sun seemed to shine even brighter and Heaven felt a bit closer to Earth.