Normal Distribution

lavendar_o5

A sugar factory has 2 packaging machines which operates simultaneously and independently. Machine A is 2 times faster than machine B. Mas of packets of sugar packed by machine A are distirubted normally with mean 1000 g and standard dev 4 g, whereas mass of packets of sugar packed by machinese B are distributed normally with mean 995 g and standard dev 5g

i) show that the probability of the mass of a packet of sugar that is selected randomly is less than 997 g is 0.370

ii) if a packet of sugar selected randomly has a mass less than 997g, find the probability that the packet is packed by machine B

iii) Find the probability that from 5 packets of sugar selected randomly, at least 2 packets have masses less than 997g

flash

原帖由 lavendar_o5 于 11-10-2007 12:53 AM 发表
A sugar factory has 2 packaging machines which operates simultaneously and independently. Machine A is 2 times faster than machine B. Mas of packets of sugar packed by machine A are distirubted n ...

(i) 应该是这样:

(2/3 * 0.2266) + (1/3 * 0.6554) = 0.370

(ii) 0.590

(iii) 0.609

lavendar_o5

请教一下，2及3如何做？

dunwan2tellu

(ii)

P( B | m<997) = P(B n m<997)/P(m<997)
              =(1/3 * 0.6554)/0.370
              = ....

(iii)
X ~ Bin(5,0.370)

P(X >=2 ) = 1 - P(X=0) - P(X=1)
          = 1 - 5C0 * (1-0.370)^5 - 5C1 * (0.370)(1-0.370)^4
          = ...

lavendar_o5

谢谢您