请教4题GWD

cxks01

求解释，求过程，都读不太懂题目，求什么？
A certain characteristic in a large population has a distribution that is symmetric about the mean m.If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m +d ?

At the end of each year, the value of a certain antique watch is c percent more than its value one year earlier, where c has the same value each year.If the value of the watch was k dollars on January1, 1992, and m dollars on January 1, 1994, then in terms of m and k, what was the value of the watch, in dollars, on January 1, 1995 ?

How many 4-digit positive integers are there in which all 4 digits are even?


A.625
B.600
C.500
D.400
E.256

A school administrator will assign each student in a group of n students to one of m classrooms.If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?
(1)It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it.
(2)It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it.

How many 4-digit positive integers are there in which all 4 digits are even?


A.625
B.600
C.500
D.400
E.256

A school administrator will assign each student in a group of n students to one of m classrooms.If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?
(1)It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it.
(2)It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it.

At the end of each year, the value of a certain antique watch is c percent more than its value one year earlier, where c has the same value each year.If the value of the watch was k dollars on January1, 1992, and m dollars on January 1, 1994, then in terms of m and k, what was the value of the watch, in dollars, on January 1, 1995 ?

How many 4-digit positive integers are there in which all 4 digits are even?


A.625
B.600
C.500
D.400
E.256

A school administrator will assign each student in a group of n students to one of m classrooms.If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?
(1)It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it.
(2)It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it.

How many 4-digit positive integers are there in which all 4 digits are even?


A.625
B.600
C.500
D.400
E.256

A school administrator will assign each student in a group of n students to one of m classrooms.If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?
(1)It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it.
(2)It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it.

thickhead

以下并不保证正确，只是参考！

1）  某个大样本集中有一个特征，其分布对平均值m来说对称。 如果在分布中有68%位于与平均值相差一个标准差d的范围内，那么小于m+d的分布占多少比例。

就是说一组数，平均值是m，标准差是d，并且它们都是对称于m的。在（m-d）和（m+d）之间有68%，问在大于（m+d）的占多少。

既然对称于m，那么比m大和比m小都是一半。在（m-d）和(m+d)之间有68%，那么在（m）和(m+d)之间有34%，比m+d大的就是16%。


2）  每年末，某古董表的价值比年初涨百分之c，每年c都不变。 如果在1992年1月1日其价值k元，在1994年1月1日是m元，那么用m和k来表达，表在1995年1月1日的价值是多少。

19920101是k, 19930101是k(1+c%), 19940101是k (1+c%)2, 19950101是k (1+c%)3。
所以m= k (1+c%)2, (1+c%)=(k/m)^1/2; 所以答案是[k^(5/2)]/[m^(3/2)]

3）  4位数的正整数中有多少是4个全部是偶数的。
从0-9中正好一半偶数，5个。但是第一位不能取0，所以第一位只能取4个。所以答案是4*5*5*5=600。
A.625
B.600
C.500
D.400
E.256



4） 把n个学生分配到m个班里。3 < m < 13 < n。每个班分配一个学生（看看出题很严谨），有没有可能使每个班的学生数量相同。
（1） 如果学生是3n个，可以使每个班学生数量相同。
（2）如果学生是13n个，可以使每个班学生数量相同。

也就是说，如果3n/m能除尽，是否n/m能除尽？ 这是不一定的， 因为如果m中含有一个因子是3，而n中不含，这种可能性就会出现。m在3和13之间，比如m是6，而n中只要含个2，3n就能把6除尽,如果3n中再含一个6除不尽的因子，就不行了。比如7，11等。也就是说m=6, n=14啊，22啊，就不行了。
如果13n/m能除尽，是否n/m能除尽？这是可以的，因为m<13, 所以m中肯定不含13这个因子。那么13n把m除尽，需要m中的因子在13n中都出现，也就是在n中都出现。所以n/m可以除尽。所以选B。

cxks01

以下并不保证正确，只是参考！

1）  某个大样本集中有一个特征，其分布对平均值m来说对称。 如果在分布中有68%位于与平均值相差一个标准差d的范围内，那么小于m+d的分布占多少比例。

就是说一组数，平均值是m，标准差是d，并且它们都是对称于m的。在（m-d）和（m+d）之间有68%，问在大于（m+d）的占多少。

既然对称于m，那么比m大和比m小都是一半。在（m-d）和(m+d)之间有68%，那么在（m）和(m+d)之间有34%，比m+d大的就是16%。

非常感谢你的解答，很清晰，答案都是正确答案，现在明白了，真的非常感谢！

2）  每年末，某古董表的价值比年初涨百分之c，每年c都不变。 如果在1992年1月1日其价值k元，在1994年1月1日是m元，那么用m和k来表达，表在1995年1月1日的价值是多少。

19920101是k, 19930101是k(1+c%), 19940101是k (1+c%)2, 19950101是k (1+c%)3。
所以m= k (1+c%)2, (1+c%)=(k/m)^1/2; 所以答案是[k^(5/2)]/[m^(3/2)]

3）  4位数的正整数中有多少是4个全部是偶数的。
从0-9中正好一半偶数，5个。但是第一位不能取0，所以第一位只能取4个。所以答案是4*5*5*5=600。
A.625
B.600
C.500
D.400
E.256



4） 把n个学生分配到m个班里。3 < m < 13 < n。每个班分配一个学生（看看出题很严谨），有没有可能使每个班的学生数量相同。
（1） 如果学生是3n个，可以使每个班学生数量相同。
（2）如果学生是13n个，可以使每个班学生数量相同。

也就是说，如果3n/m能除尽，是否n/m能除尽？ 这是不一定的， 因为如果m中含有一个因子是3，而n中不含，这种可能性就会出现。m在3和13之间，比如m是6，而n中只要含个2，3n就能把6除尽,如果3n中再含一个6除不尽的因子，就不行了。比如7，11等。也就是说m=6, n=14啊，22啊，就不行了。
如果13n/m能除尽，是否n/m能除尽？这是可以的，因为m<13, 所以m中肯定不含13这个因子。那么13n把m除尽，需要m中的因子在13n中都出现，也就是在n中都出现。所以n/m可以除尽。所以选B。

-- by 会员 thickhead (2011/11/30 21:19:45)

cxks01

非常感谢你的解答，很清晰，答案都是正确答案，现在明白了，真的非常感谢！

viota

5*5*5*4=500.    

eminem1101

弟三题计算有误
4*5*5*5=500