问题 解答题
某公司共有职工8000名,从中随机抽取了100名,调查上、下班乘车所用时间,得下表:
所用时间(分钟)[0,20)[20,40)[40,60)[60,80)[80,100)
人数25501555
公司规定,按照乘车所用时间每月发给职工路途补贴,补贴金额Y (元)与乘车时间t (分钟)的关系是y=200+40[
t
20
]
,其中[
t
20
]
表示不超过[
t
20
]
的最大整数.以样本频率为概率:
(I)估算公司每月用于路途补贴的费用总额(元);
(II)以样本频率作为概率,求随机选取四名职工,至少冇两名路途补贴超过300 元的概率.
答案

(Ⅰ)记一名职工所享受的路途补贴为X(元).

X的可能值为200,240,280,320,360.

X的分布列为

X200240280320360
P0.250.50.150.050.05
X的均值为E(X)=200×0.25+240×0.5+280×0.15+(320+360)×0.05=246.…(5分)

该公司每月用于路途补贴的费用总额约为E(8000X)=8000E(X)=1968000(元).…(7分)

(Ⅱ)依题意,当60≤t≤100时,y>300.

1名职工中路途补贴超过300元的概率P=P(60≤t≤100)=0.1,…(8分)

记事件“4名职工中至少有2名路途补贴超过300元”为A,则

P(A)=

C24
×0.12×0.92+
C34
×0.13×0.9+0.14=0.0523.…(12分)

选择题
单项选择题

With unemployment rising and housing costs still high, cities around the country are experiencing a new and sudden wave of homelessness. Shelters are overflowing, and more people this year are sleeping on floors in dingy social service centers, living in cars or spending nights on the streets.

In New York, Boston and other cities, homelessness is at record levels, a consequence of a faltering (摇晃的) economy that has crumbled even further after the Sept.11 attacks.

A survey by the U. S. Conference of Mayors released last week found that requests for emergency shelter in 27 cities had increased an average of 13 percent over last year. The report said the increases were 26 percent in Trenton; 25 percent in Kansas City, Mo.; 22 percent in Chicago; 20 percent in Denver; and 20 percent in New Orleans.

An unusual confluence of factors seems to be responsible for the surge. Housing prices, which soared in the expansion of the 1990’s, have not gone down, even though the economy has tumbled. A stream of layoffs has newly unemployed people taking low-wage jobs that might have otherwise gone to the poor. Benefits for welfare recipients are expiring under government-imposed deadlines. And charitable donations to programs that help the disadvantaged are down considerably, officials around the country said, because of the economy and the outpouring of donations for people affected by Sept.11.

"This is an unprecedented convergence (集中) of calamities (灾难), " said Xavier De Souza Briggs, an assistant professor of public policy at the John F. Kennedy School of Government at Harvard. "It’s really a crisis. "

More than half the cities surveyed by the mayors’ group reported that in the last year people had remained homeless longer, an average of six months.

There is no total number for the homeless nationwide. Experts said it was difficult to compare the situation with statistics in previous decades, because counting methods have improved. Yet, several experts said they believed that the increases reported by cities like Boston and Chicago reflected a national trend.

"My impression is there is more homelessness now than there was 20 years ago, " Gary Burtless, an economist at the Brookings Institution, said, adding that he believed that economic factors were not the sole explanation.

"I think that there must be a greater segment of our population that has tenuous connections to family and friends, and therefore has fewer resources to fall back on when something very bad happens like when they lose their job, " he said.

According to economist Gary Burtless, What factor accounts for the surge of homeless apart from the economic explanation().

A. Political.

B. Social.

C. Religious.

D. International.