用正态分布逼近做,某厂有400台同类机器,各台机器发生故障的概率均为0.02,假设各台机器工 作是相

用正态分布逼近做,某厂有400台同类机器,各台机器发生故障的概率均为0.02,假设各台机器工 作是相

这是一个概率上的中心极限定理问题,400台每台发生概率为0.02,就服从二项分布b（400,0.02）,在n很大（这里是400）时,二项分布就近似服从正态分布了,那么故障数大于2的概率p(X>2)=p( (X-400*0.02)/(400*0.02*(1-0.02))^(1/2)>(2-400*0.02)/(400*0.02*(1-0.02))^(1/2) )=1-Fai((2-400*0.02)/(400*0.02*(1-0.02))^(1/2) )=1-Fai(2.8)=1-0.9974449=0.00255513.其中的,X为故障数,是一个随机变量,精确分布为二项分布b（400,0.02）,渐近分布为正态分布,这个在教材上有定理,p表示概率,*表示乘法,^表示乘方,比如3^2=9,Fai为标准正态分布的分布函数.如果还看不清楚留下你的邮箱发给你答案.======以下答案可供参考======供参考答案1:你这题标准泊松分布的例题，用正态分布的原因是什么？供参考答案2:Junior middle school mathematical probability preliminary since have preliminary two characters, obviously will have more deep content, and now is the foundation of knowledge base, in the life, probability applying is also is very wide, especially for some things that, for some data statistics, all need to use. So, you must first learn to preliminary understanding of junior middle school mathematical probability preliminary way of thinking, and then, to see tests review requirements.1, understanding what is inevitable happen events, don't happen, what is random events.2, in specific situation in understanding the meaning of probability, realize probability is to describe the rule of uncertain phenomenon, the mathematical model of understandingThe value scope of the probability of the meaning, the development of random idea. ·

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