# 計算題統計學樣本平均數變異數標準差

1A random sample of size 100 were selected from a population with mean 10 and variace 9 . Find the mean and standard deviation of the sampling distribution of the sample mean and also find the probability that the sample mean is less than 10.2.

2A survey was taken of 313 children,ages 14 to 22 years,from among the children of the nation\'s top corporate executives. When asked to identify the best aspect of being one of this privileged group,55% mentioned material and financial advantages. Suppose that the proportion p of children in the population is actually equal to 0.5. What is the probability of observing a sample proportion as large as or larger than the obsevred

^

value P=0.55?

3Twelve measurements were randomly selected from a normal population with mean

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and standard deviation, 125.12 and 12.3, respectively. find P(X>130)?

Rating

1.

n=100(n>30)~Z, use the Central Limit Theorem

ｘ－ｂａｒ=10, σ=9

p(ｘ－ｂａｒ<10.2)=p[z<10.2-10/(9/√100)]=p(z<2/9)

2.p=0.5,σ=√p(1-p) =√0.5(1-0.5)

p[p>0.55]=p[z>0.55-0.5/√0.5(1-0.5)/√313]=p[z>0.05/(√0.25/√313)]

3.n=12,∵ the measurements from a normal population

∴use the normal distribution

P(X>130)=p[z>130-125.12/(12.3/12)]

2006-08-04 02:11:55 補充：

是啊 我打錯了應該是σ平方=9

σ=３