题目
A particular lift has a maximum load capacity of 700 kg. The weights of men are normally distributed with mean 80 kg and standard deviation 10 kg. The weights of women are normally distributed with mean 69 kg and standard deviation 5 kg. You may assume that weights of people are independent.
(a) Find the probability that when 6 men and 3 women are in the lift, the load exceeds 700 kg.
A sign in the lift states: “Maximum number of people in the lift is c”
(b) Find the value of c such that the probability of the load exceeding 700 kg is less than 2.5% no matter the gender of the occupants.
题目中文翻译
一部电梯的最大载重为 700 千克。 男性体重服从均值 80 千克、标准差 10 千克的正态分布。 女性体重服从均值 69 千克、标准差 5 千克的正态分布。 你可以假设人的体重相互独立。
(a) 求当电梯中有 6 名男性和 3 名女性时，载重超过 700 千克的概率。
电梯内的标牌写着：“电梯中的最大人数为 c”
(b) 求 c 的值，使得无论乘客性别如何，载重超过 700 千克的概率都小于 2.5%。