The mass of a grade A steel cylinder manufactured in a factory follows a normal distribution with mThe mass of a grade A steel cylinder manufactured in a factory follows a normal distribution with mean 2.2 kg and standard deviation 250 g.The mass of

Question

The mass of a grade A steel cylinder manufactured in a factory follows a normal distribution with m
The mass of a grade A steel cylinder manufactured in a factory follows a normal distribution with mean 2.2 kg and standard deviation 250 g.The mass of a grade B steel follows a normal distribution with mean 1.5 kg and standard deviation 140 g.Determine the probability that
求the total mass of 6 grade A steel is more than that of 7 grade B steel,all chosen at random.

Answer 1

A 服从高斯分布G(2.2,0.25)；B 服从高斯分布G(1.5,0.14).
定义
Y = 6A-7B,
则Y服从高斯分布G(2.7,0.71568).
所以
P（Y > -2.7） = P (Y/0.71568 > -3.77) = 0.999918.