想必現(xiàn)在有很多小伙伴對于生產(chǎn)工藝工程中產(chǎn)品的尺寸偏差$X\left(mm\right)\sim N\left(0,2^{2}\right)$，如果產(chǎn)品的尺寸與現(xiàn)實(shí)的尺寸偏差的絕對值不超過$4mm$的為合格品，求生產(chǎn)$5$件產(chǎn)品的合格率不小于$80\%$的概率.(精確到$0.001)\left(\left(0.954?4\right)^{5}\approx 0.791?9;\left(0.954?4\right)^{4}\approx 0.8297\right)$","title_text":"生產(chǎn)工藝工程中產(chǎn)品的尺寸偏差$X\left(mm\right)\sim N\left(0,2^{2}\right)$，如果產(chǎn)品的尺寸與現(xiàn)實(shí)的尺寸偏差的絕對值不超過$4mm$的為合格品，求生產(chǎn)$5$件產(chǎn)品的合格率不小于$80\%$的概率.(精確到$0.001)\left(\left(0.954?4\right)^{5}\approx 0.791?9;\left(0.954?4\right)^{4}\approx 0.8297\right)$方面的知識都比較想要了解，那么今天小好小編就為大家收集了一些關(guān)于生產(chǎn)工藝工程中產(chǎn)品的尺寸偏差$X\left(mm\right)\sim N\left(0,2^{2}\right)$，如果產(chǎn)品的尺寸與現(xiàn)實(shí)的尺寸偏差的絕對值不超過$4mm$的為合格品，求生產(chǎn)$5$件產(chǎn)品的合格率不小于$80\%$的概率.(精確到$0.001)\left(\left(0.954?4\right)^{5}\approx 0.791?9;\left(0.954?4\right)^{4}\approx 0.8297\right)$","title_text":"生產(chǎn)工藝工程中產(chǎn)品的尺寸偏差$X\left(mm\right)\sim N\left(0,2^{2}\right)$，如果產(chǎn)品的尺寸與現(xiàn)實(shí)的尺寸偏差的絕對值不超過$4mm$的為合格品，求生產(chǎn)$5$件產(chǎn)品的合格率不小于$80\%$的概率.(精確到$0.001)\left(\left(0.954?4\right)^{5}\approx 0.791?9;\left(0.954?4\right)^{4}\approx 0.8297\right)$方面的知識分享給大家，希望大家會喜歡哦。

解由題意$Xsim Nleft(0,2^{2}right)$，求得$Pleft(|X|leqslant 4right)=Pleft(-4leqslant Xleqslant 4right)=0.954?4$.

設(shè)$Y$表示$5$件產(chǎn)品中合格品個(gè)數(shù)，則$Ysim Bleft(5,0.954?4right)$.

$therefore Pleft(Ygeqslant 5times 0.8right)=Pleft(Ygeqslant 4right)=C_{5}^{4}times left(0.9544right)^{4}times 0.045?6+C_{5}^{5}times left(0.9544right)^{5}approx 0.1892+0.7919approx 0.981$.

故生產(chǎn)的$5$件產(chǎn)品的合格率不小于$80%$的概率約為$0.981$.

本文到此結(jié)束，希望對大家有所幫助。