S5 Maths. (compulsory Part)

2013-06-19 2:28 am

Please to help slove the following maths. questions

1. A student is randomly selected from the group. Find the probability that
the score of the selected students is not greater than 65.

2. If the standard deviation of a, b, c, d and e is k, find the standard deviation
of 5a - 4, 5b - 4. 5c - 4, 5d - 4 and 5e -4

3. If the mean of the data set A: ( 7, 9, 15, 18, 20, m, n) is 14 and m and n are
both positive integers, which of the following must be true?
I. Range of the data set A<28
II. Median of the data set A = 15
III. If the datum "15" is removed from the data set, the mean will increase

4.The mean and the standard deviation of a group of 20 numbers are
10 and 2 respectively. When two more numbers, both are 10, are added,
the group of numbers has
a. mean = 10, standard deviation =2
b. mean = 10, standard deviation <2
c. mean > 10, standard deviation =2
d. mean < 10, standard deviation > 2

回答 (1)

Herman Tam

2013-06-19 9:55 am

✔ 最佳答案

Question 2
var(x)=k^2
var(5x-4)=var(5x)=25var(x)=25k^2
sd(5x-4)=sqrt[var(5x-4)]=5k

the sd of 5a-4, 5b-4, 5c-4, 5d-4 and 5e-4 is 5k

Question 3
7+9+15+18+20+m+n=69+m+n
if mean = 14, m+n=14*(7)-69=98-69=29
the largest range can only be 28-1=27
Statement I must not be true

if m=<15 and n>=15, the mean will be 15
since m+n=29,
there is no comination of (m,n) which can violate m<=15 and n>=15
Statement II must be true

Since the mean is 14, if a number larger than 14 is removed, the mean will decrease.
Statement III must not be true

Question 4
Mean will still be unchanged if number equal to mean is added.
Standard deviation will be reduced if number equal to mean is added, i.e. <2
explanation:
sd = sqrt[ sum of variance/ total number]
when number equal to mean is added,
sum of variance unchanged
total number increase
sd hence reduced

參考: ME

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