【問題】会英語会統計的高手入来帮下手。。拜托。

[xdongx 10]

1.The following information about the number of persons per family in Canada is provided by Statistics Canada (Census 1990),*

Number of persons per family Percent of families (%)

2 persons 43.51

3 persons 22.61

4 persons 23.07

5 persons 8.38

6 persons 2.02

7 persons 0.41

* Number of persons per families with more than 7 persons is negligible. Their probability is taken to be zero.

(a)Compute the probability of three or fewer persons per family.

(b)Compute the expected number of persons per family.

©Compute the standard deviation of the number of persons per family.

(d)Graph the above probability distribution.

2.normal distribution has a mean of 50 and a standard deviation of 4. Determine the value below which 95 percent of the observations will occur.

[mapleaf 11]

(a)Compute the probability of three or fewer persons per family

Ans: P(x=2)+P(x=3)=43.51%+ 22.61%=0.4351+0.2261=0.6612

[mapleaf 11]

(b)Compute the expected number of persons per family.

Ans:

E(x)=2 *P(x=2)+3*P(x=3)+4* P(x=4)+5 *P(x=5)+6 *P(x=6)+7*P(x=7)

= 2 * 0.4351+3 * 0.2261+4* 0.2307+5 *0.0838+6 *0.0202+7*0.0041=3.0402

[mapleaf 11]

©Compute the standard deviation of the number of persons per family

Ans:

standard deviation =sigma=Square Root of Variance

Var(x)=E(x^2)-[E(x)]^2

= [4 * 0.4351+9 * 0.2261+16* 0.2307+25 *0.0838+36 *0.0202+49*0.0041]-[3.0402]^2

=10.4896-9.242816=1.246784

Sigma=[Var(x)]^0.5=1.116595

[mapleaf 11]

(d)Graph the above probability distribution.

[mapleaf 11]

2.normal distribution has a mean of 50 and a standard deviation of 4. Determine the value below which 95 percent of the observations will occur.

Excel: NORMSINV(0.95)= 1.644853476= z

By z=(x-mu)/sigma

1.644853476=(x-50)/4

x =56.579413903

[00 10]

©Compute the standard deviation of the number of persons per family

Ans:

standard deviation =sigma=Square Root of Variance

Var(x)=E(x^2)-[E(x)]^2

= [4 * 0.4351+9 * 0.2261+16* 0.2307+25 *0.0838+36 *0.0202+49*0.0041]-[3.0402]^2

=10.4896-9.242816=1.246784

Sigma=[Var(x)]^0.5=1.116595

這個能不能解釋一下，我不太懂，謝謝。

[00 10]

2.normal distribution has a mean of 50 and a standard deviation of 4. Determine the value below which 95 percent of the observations will occur.

Excel: NORMSINV(0.95)= 1.644853476= z

By z=(x-mu)/sigma

1.644853476=(x-50)/4

x =56.579413903

x應該是一個範圍吧（56.多>x>43.多），如果我弄錯請指正，謝謝。

[Zeta 10]

1.The following information about the number of persons per family in Canada is provided by Statistics Canada (Census 1990),*

Number of persons per family Percent of families (%)

2 persons 43.51

3 persons 22.61

4 persons 23.07

5 persons 8.38

6 persons 2.02

7 persons 0.41

* Number of persons per families with more than 7 persons is negligible. Their probability is taken to be zero.

(a)Compute the probability of three or fewer persons per family.

(b)Compute the expected number of persons per family.

©Compute the standard deviation of the number of persons per family.

(d)Graph the above probability distribution.

2.normal distribution has a mean of 50 and a standard deviation of 4. Determine the value below which 95 percent of the observations will occur.

嗯,這些應該是初等統計學的東西吧,我有接觸一點點啦,我沒有很清楚:E

期望值,標準差,常態分佈,機率這些應該都是

要做圖的話,你用origin,sigmaplot搭配excel就很夠了:p

要專業一點的話,你去用SPSS好了

[mapleaf 11]

這個能不能解釋一下，我不太懂，謝謝。

題目的意思是說有一個mu(平均數)=50,Sigma(標準差)=4,服從常態分配的曲線,要尋找一個值x,而x之下的資料佔有百分之九十五

我先利用Excel,先找到"標準常態分配",的Z值

標準常態分配mu(平均數)=0,Sigma(標準差)=1,

在Excel任意儲存格打"=NORMSINV(0.95)",將出現1.644853476,這就是Z值

再以轉換公式Z=(x-mu)/Sigma, 即可求出其對應的x

[xdongx 10]

thank for your help .............

:'( ~~~~~~~~~~~`