题干

某校高三年级文科学生600名,从参加期末考试的学生中随机抽出某班学生(该班共50名同学),并统计了他们的数学成绩(成绩均为整数且满分为150分),数学成绩分组及各组频数如下表:

分组

频数

频率

[45,60)

2

0.04

[60,75)

4

0.08

[75,90)

8

0.16

[90,105)

11

0.22

[105,120)

15

0.30

[120,135)

a

b

[135,150]

4

0.08

合计

50

1

(1)写出a、b的值;

(2)估计该校文科生数学成绩在120分以上学生人数;

(3)该班为提高整体数学成绩,决定成立“二帮一”小组,即从成绩在[135,150]中选两位同学,来帮助成绩在[45,60)中的某一位同学.已知甲同学的成绩为56分,乙同学的成绩为145分,求甲乙在同一小组的概率.

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答案(点此获取答案解析)

解:(1)频率总数是1,所以所缺频率b=1﹣(0.04+0.08+0.16+0.22+0.30+0.08)=0.12.

第6行的频数=50×0.12=6;

∴a、b的值分别为:6、0.12

(2)成绩在1(20分)以上的有6+4=10人,

所以估计该校文科生数学成绩在1(20分)以上的学生有:1050

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