统计学的计算题,重金求大神赐教!急求!

题目

统计学的计算题,重金求大神赐教!急求!
一个电脑制造商想检验一个元件的寿命.根据经验,寿命的平均值μ=117天,寿命的标准差σ=2.1天.假设寿命是正态分布的.1.随机抽取1个元件的寿命必120天长的概率. 2.随机抽取3个元件寿命都超过120天的概率 3.随机抽取3个元件平均寿命在114-120天之间的概率 4.随机抽取三个元件,平均寿命超过120的概率
PS：这是英文原题 A computer manufacturer wants to check the lifetime to of a component. According the experience, the mean value of the lifetime is = 117 days and the standard deviation of the lifetime is =2.1 days. Assuming the lifetime is normally distributed.
i. What the probability a random selected component has a lifetime longer than 120 days?
ii. What the probability that if 3 components are selected, all the three components’ lifetime exceeding 120 days?
iii. What the probability that if 3 components are selected, the average lifetime of the three components is between 114 and 120 days?
iv .What the probability that if 3 components are selected, the average lifetime of the three components exceeding 120 days?

答案

这个是随机正态分布：先由提议可知：平均值为117填,根据正态分布先求Φ(120-117)/2.1≈0.9236这上面求的是小于120天得概率：则：1.随机抽取1个元件的寿命必120天长的概率：1-0.9236=0.07642.随机抽取3个元件寿命都超...