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86题是一道关于中心极限定律的题，原题如下
86. A city has just added 100 new female recruits to its police force. The city will provide a
pension to each new hire who remains with the force until retirement. In addition, if the
new hire is married at the time of her retirement, a second pension will be provided for
her husband. A consulting actuary makes the following assumptions:
(i) Each new recruit has a 0.4 probability of remaining with
the police force until retirement.
(ii) Given that a new recruit reaches retirement with the police
force, the probability that she is not married at the time of
retirement is 0.25.
(iii) The events of different new hires reaching retirement and the
events of different new hires being married at retirement are all
mutually independent events.
Calculate the probability that the city will provide at most 90 pensions to the 100 new
hires and their husbands.
(A) 0.60
(B) 0.67
(C) 0.75
(D) 0.93
(E) 0.99
这个题目的解答如下
For a single recruit, the probability of 0 pensions is 0.6, of 1 pension is 0.4(0.25) = 0.1, and of 2
pensions is 0.4(0.75) = 0.3. The expected number of pensions is 0(0.6) + 1(0.1) + 2(0.3) = 0.7.
The second moment is 0(0.6) + 1(0.1) + 4(0.3) = 1.3. The variance is 1.3 – 0.49 = 0.81. For 100
recruits the mean is 70 and the variance is 81. The probability of providing at most 90 pensions
is (with a continuity correction) the probability of being below 90.5. This is (90.5 – 70)/9 = 2.28
standard deviations above the mean. From the tables, this probability is 0.9887.
请大家看红色标出的部分，原题中问的是最多给付90份pensions的概率，为何答案中将这个概率等价为不小于90.5份pensions的概率，另外括号中的continuity correction是什么意思？
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