STPM-学校功课討論区

zfc

我有maths T, data description这个chapter的问题要问，希望高手能帮忙。

The lifespan (in hours) for a certain type of batteries is measured by taking a sample of 100 batteries and the result are given below.

Lifespan(hours)	90	95	100	105	110	115	120	125	130
Frequency	2	17	30	21	15	9	3	2	1

Estimate the fraction of batteries that have lifespans within one standard deviation from the mean.

答案：33/50

这是我的想法：
mean=104.25
fraction of batteries within 1 standard deviation的意思就是把lifespan 100、105和110的frequency就起来over 100，所以=66/100=33/50.
我的想法对不对呢？Within 1 standard deviation的真正定义何在？

[ 本帖最后由 zfc 于 14-10-2007 09:54 AM 编辑 ]

Leong13

你的做法对可是应该这样写出来

standard deviation = 6.43
mean = 104.25

104.25 - 6.43< x < 104.25 + 6.43

97.82 < x < 110.68
97.82 < 100, 105, 110 < 110.68

(30 + 21 + 15)/100 = 33/50

zfc

原帖由 Leong13 于 14-10-2007 04:29 PM 发表
你的做法对可是应该这样写出来

standard deviation = 6.43
mean = 104.25

104.25 - 6.43< x < 104.25 + 6.43

97.82 < x < 110.68
97.82 < 100, 105, 110 < 110.68

(30 + 21 + 15)/100 = 33/50

哦，谢谢你。
我还以为within one standard deviation的意思是standard deviation=1。

Leong13

答案不對，書給的答案 ＝ ０．０２１２８

sardinecan

leong13
你用的书是不是federal study aids mathematics T
pg 290 q39的问题？一样的题目， 答案是0.203
先找了P(X=0)=e^-3=0.04979
然后,5C1(0.04979)(1-0.04979)^4=0.203

flash

如果题目是像我了解的那样，答案不应该是这样。。。。应该是 0.203，不好意思之前算错了。

Leong13

我是用這本書，那是書給錯答案嗎？

Leong13

請問有沒有人幫忙solve４３７樓的問題。

dunwan2tellu

原帖由 Leong13 于 10-10-2007 03:10 PM 发表
1. an electrical appliance shop has 4
   television sets for rental on a monthly
   basis. the number of televisions
   requested by customers in one month
   follows a poisson distribution  ...

1)
P(X=x) = e^(-3)*3^x/x!

E(X) = 1*P(X=1)+2*(PX=2)+3*(PX=3)+4*P(X>=4)
     = ....


2) probability of correct call , p = 0.999

number of call = n ,

p^n =< 0.1

n >= ....

Leong13

1.floor tiles are manufactured in two
  sizes, large and small. the mass of a
  large tile is distributed normallly with
  mean 30 kg and standard deviation 0.5 kg.
  the mass of a small tile is distributed
  normally with mean 14.5 kg and standard
  deviation 0.25 kg.
i) a man buys a number of large tiles  
   and small tiles for his compound.
   he finds that his orger exceeded
   his needs slightly so that either
   a large tile or two small tiles
   will not be used. by assuming
   that the probability of either
   of the two alternatives is the
   same , find the probability
   that the mass of the remaining
   tile(s) will exceed 29.5 kg

lavendar_o5

If the straight line y = mx + c is a tangent to the x^2 / a^2 + y^2 / b^2 = 1 , show that c^2 = a^2m^2 + b^2

Find the gradient of the tangent to the curve which passes through the point sqrt(a^2+b^2), 0. Hence determine the corrdinates of the vertices of the square whose sides touch the curve.

c^2 = a^2m^2 + b^2我已解。Find the gradient of tangent to the curve，我算到m = +-1，是吗？再下一part真的不知道如何做了。。。

lavendar_o5

关于第二part找Gradient of tangent (也就是dy / dx)，我就用dy/dx方式找，为什么不能用呢：

x^2 / a^2 +y^2 / b^2 = 1
2x / a^2 + 2y ( dy / dx ) / b^2 = 0
subs x = sqrt (a^2 + b ^2) , y = 0进去
当y = 0放进去，dy / dx 都不见了。。。怎么用dy/dx方式找呢？

dunwan2tellu

原帖由 lavendar_o5 于 19-10-2007 09:36 PM 发表
If the straight line y = mx + c is a tangent to the x^2 / a^2 + y^2 / b^2 = 1 , show that c^2 = a^2m^2 + b^2

Find the gradient of the tangent to the curve which passes through the point sqrt(a ...

m = +-1 是对的

运用之前得到的资料 ：
考虑 coordinate (sqrt[a2+b2],0) .从这个点 tangent to curve 的 line 的 equation

y = x + c  或  y = -x + c (因为 m = +-1)

因为它经过 (sqrt[a2+b2],0) 所以 c = + - sqrt[a2+b2]

所以他的 y-intercept 是 (0,sqrt[a2+b2]) 和 (0,- sqrt[a2+b2])

同样的再拿点 (-sqrt[a2+b2],0) ,那么这 4 个点就是 vertices of square .而且都 tangent to the curve (以图画来看想是 diamond 的形状）

原帖由 lavendar_o5 于 19-10-2007 09:43 PM 发表
关于第二part找Gradient of tangent (也就是dy / dx)，我就用dy/dx方式找，为什么不能用呢：

x^2 / a^2 +y^2 / b^2 = 1
2x / a^2 + 2y ( dy / dx ) / b^2 = 0
subs x = sqrt (a^2 + b ^2) , y = 0进去
当 ...

因为 (sqrt[a2+b2],0) 都不是 curve 上面的 point（她是在 curve 的外面） ,所以你不可以直接 substitute 进去。

补充： (sqrt[a2+b2],0) 只是 line 经过的 point , 不是 curve 经过的 point

[ 本帖最后由 dunwan2tellu 于 20-10-2007 11:09 AM 编辑 ]

lavendar_o5

原帖由 dunwan2tellu 于 20-10-2007 11:08 AM 发表


m = +-1 是对的

运用之前得到的资料 ：
考虑 coordinate (sqrt[a2+b2],0) .从这个点 tangent to curve 的 line 的 equation

y = x + c  或  y = -x + c (因为 m = +-1)

因为它经过 (sqrt[a2+b2] ...

真的谢谢您！我怎么没看出它是LINE的点，而不是Curve的点呢。。。真笨。。哈哈

lavendar_o5

再来一题:

The straight line y = mx – 4 meets the curve y^2 = 8x at 2 distinct points A (x1, y1) and B(x2, y2). Show that

(a)        x1+y1=(8m+8)/m
If O is the origin and C is a point such that OACB is a parallelogram, show that as m varies, the equation of the locus of C is y^2 +8y=8x

是否题目有误？我怎么算，x1+y1都不可能等于(8m+8)/m

dunwan2tellu

原帖由 lavendar_o5 于 20-10-2007 02:10 PM 发表
The straight line y = mx – 4 meets the curve y^2 = 8x at 2 distinct points A (x1, y1) and B(x2, y2). Show that

(a)        x1+y1=(8m+8)/m
If O is the origin and C is a point such that OACB is a parallelogram, show that as m varies, the equation of the locus of C is y^2 +8y=8x

是否题目有误？我怎么算，x1+y1都不可能等于(8m+8)/m

正确来说应该是

x1 + x2 = (8m + 8)/m^2
方法并不难，只需要考虑 sum of roots of quadratic equation (mx-4)^2 = 8x

如果是 x1,y1 的话 应该是

x1 + y1 = (8m + 4) + - 8*sqrt[2m+1]

第2part , 用 midpoint of AB = midpoint of OC 和 y1 + y2 = 8/m 来找

[ 本帖最后由 dunwan2tellu 于 20-10-2007 04:00 PM 编辑 ]

lavendar_o5

A family consisting of the father and seven other members. Each time a holiday trip is suggested, the father and the family members must accept or reject it. The probability that the father will accept a holiday trip is 4 / 5 . The other members make their decision independently, but the probability that each member agrees with the father is 3 / 4 . A holiday trip is agreed by the family members when the number of members who accept it exceeds the number of members who oppose it, or if the number of members who accept it is equal to the number who oppose it and the father is among those who accept it.

1        Find the probability that a holiday trip is agreed by the family members if the father oppose it
2        Find the probability that a holiday trip is agreed by the family members.

flash

原帖由 lavendar_o5 于 21-10-2007 09:23 AM 发表
A family consisting of the father and seven other members. Each time a holiday trip is suggested, the father and the family members must accept or reject it. The probability that the father will  ...

算到

1. 0.013
2. 0.792

Leong13

有沒有人幫我作４５０樓的問題？？？

lavendar_o5

原帖由 flash 于 21-10-2007 06:23 PM 发表



算到

1. 0.013
2. 0.792

请问如何算呢？