統(tǒng)計(jì)學(xué)的計(jì)算題,重金求大神賜教!急求!
一個(gè)電腦制造商想檢驗(yàn)一個(gè)元件的壽命.根據(jù)經(jīng)驗(yàn),壽命的平均值μ=117天,壽命的標(biāo)準(zhǔn)差σ=2.1天.假設(shè)壽命是正態(tài)分布的.1.隨機(jī)抽取1個(gè)元件的壽命必120天長的概率. 2.隨機(jī)抽取3個(gè)元件壽命都超過120天的概率 3.隨機(jī)抽取3個(gè)元件平均壽命在114-120天之間的概率 4.隨機(jī)抽取三個(gè)元件,平均壽命超過120的概率
PS：這是英文原題 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?