问一道统计学问题：英文Suppose a population has a mean of 90 and a standard deviation of 28.If a random sample of size 49 is drawn from the population,the probability of drawing a sample with a mean of more than 95 is _________ .Select one:a.0.3944b.1.0000c.0.8944d.0.4286e.0.1056我总觉得是a,但是不是应该X2的吗?为什么?
问题描述：
问一道统计学问题：英文
Suppose a population has a mean of 90 and a standard deviation of 28.If a random sample of size 49 is drawn from the population,the probability of
drawing a sample with a mean of more than 95 is _________ .
Select one:
a.0.3944
b.1.0000
c.0.8944
d.0.4286
e.0.1056
我总觉得是a,但是不是应该X2的吗?为什么?
答
还是先翻译成中文吧，平均值90 标准差28
取出一个49个的样本，样本均值大于95的概率是多少？
利用中心极限定理
p(x>95)=1-p(x=1-z[(95-90)/(28/√49)]=1-z(5/4)=1-0.8943=0.1057
我觉得你可以再看看中心极限定理，要求的是均值大于95的概率，因此直接根据中心极限定理转化成标准正态来求解即可。
答
e
因为u=(95-90)/(28/√49)=1.25,查表得P=0.056 .