题干

某市政府为了引导居民合理用水,决定全面实施阶梯水价,阶梯水价原则上以住宅(一套住宅为一户)的月用水量为基准定价:若用水量不超过12吨时,按4元/吨计算水费;若用水量超过12吨且不超过14吨时,超过12吨部分按6.60元/吨计算水费;若用水量超过14吨时,超过14吨部分按7.80元/吨计算水费.为了了解全市居民月用水量的分布情况,通过抽样,获得了100户居民的月用水量(单位:吨),将数据按照[0,2],(2,4],…,(14,16]分成8组,制成了如图1所示的频率分布直方图.

(Ⅰ)假设用抽到的100户居民月用水量作为样本估计全市的居民用水情况.

( i)现从全市居民中依次随机抽取5户,求这5户居民恰好3户居民的月用水用量都超过12吨的概率;

(ⅱ)试估计全市居民用水价格的期望(精确到0.01);

(Ⅱ)如图2是该市居民李某2016年1~6月份的月用水费y(元)与月份x的散点图,其拟合的线性回归方程是 y^=2x+33 .若李某2016年1~7月份水费总支出为294.6元,试估计李某7月份的用水吨数.

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答案(点此获取答案解析)

解:(Ⅰ)( i)由题意,从全市居民中依次随机抽取5户,每户居民月用水量超过12吨的概率为 10
1
,因此这5户居民恰好3户居民的月用水用量都这超过12吨的概率为

同类题5

完形填空

    One autumn morning, I spotted a pair of wild geese on our pond. The beautiful sight caught me by 1 because I'd never seen geese there before. Thinking they would soon leave, I 2 the chance to get close to them. I wondered where they came from and why they had chosen our pond.

    The next morning, the geese were still my 3 I walked round to the mailbox, showing them I meant no harm4I couldn't resist getting a 5 look. I hid behind some trees and 6 the handsome pair quietly through the branches. I was surprised to see they were staring at me, too!

    As days passed, I started 7 to them on my trips to the mailbox. They craned (伸长) their necks and raised their heads 8 but seemed to realize I was their friend. By then, my curiosity about 9 they were staying so long at the pond changed to10. As they were feeding in the grass the other day, I discovered the reason for their 11the male had a broken left wing. He couldn't 12 and his faithful mate wouldn't leave him behind. I asked a biologist what to do. He explained that sometimes a13 wing will heal by itself and suggested letting nature take its course.

    On the first day of November, I was working in the neighborhood of the geese with my tractor. As I bent to fasten a chain from the tractor, I 14some movement from the corner of my eye. Both geese were running towards the pond. Their wings were 15 like crazy, struggling for take off. Gradually, they flew over the pond. They16 enough altitude to fly past a neighbor's house, and then circled back towards me, flying no more than 50 feet over my head as if to say goodbye. Then they were out of my17.

    The season's first snowflakes fell the very next day. The birds must have 18 that winter was coming, and it was time to go. I became fond of them during their 19 visit to our pond, and now I miss them. I'll never forget their 20 to each other.

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