報日僑華
六期星日四廿月三(〇九九一年九十七國民華中
風南:
(a) Fill in the table below.
3. (a)
Range of marks
Number of candidates who score x
Marks
Number of students with marks below this mark.
0 x 10
4
10 6 x < 20
5
10
20 < x < 30
10
20
30 < x < 40
20
30
40 < x < 50
28
40
50 < x < 60
20
W. K. Lei
50
60 × 470
60
70 $ x.< 80
8
4
1990 中學會考預習專欄
Mathematics (25)
選出版社
MILL & DALE PRESS
Exercise 25: Experimental probability and statistics
1. loaded die is thrown 1000 times. The frequencies of the
numbers which turn up are given in the following table.
(b) Deteraine, from the graph,
Table 5
(b) 25% of the candidates failed in the test 75 candidates above
or equal to 32.5
i.
The pass mark, if the pass percentage is 45%
.". pass mark 32.
{Ans.)
Number
Frequency
1
3
1
5
6
ii. the pass percentage if the pass mark is 25
200
100
200
100
100
300
Table 1
iii. If 95% of the students got grades lower than 'A', find
the rance of the grade.
(c) From the graph, among the candidates who score above or equal
to 32.5, there are 75 - 20 - 55 candidates with marks less than 56
.. The probability
一次。
位老友,出門去街,要想定的,否則離免爲槍下旁魂也..我第一個學期後,便供了四場音樂會,
!就被搶「殺!韭香港,令後街派分分源會有偷戰。各以每位同學演出的機會亦能應增加了。 打香港之主意者,不下三戶百人,只要他們一條說起嘭一堂的音樂會節目。因爲音樂會比較多,所 太寫張瑛道:「照戴胡亂猜測,此種大國,時刻會扣樂兵的週會熱,遠得負責非某大會, 【位,而智星期除了要自己去學的不問樂一家人,当期待
(a) When two loaded dice are thrown, what is the probability that
the sum of the two numbers shown is 107
(b) When two loaded dice are thrown, what is the probability that
botn numbers shown are even and their sum is 10?
(c) Two loaded dice are thrown, and the sum of the numbers shown is 10. What is the probability that these two numbers are buth even?'
2. The lengths of a random sample of 100 iron rods from a wharehouse
are measured and the frequency distribution is us follows
Length (in cm)
3.5-3.613.6-3.
Frequency
3.8-3.9 3.9-4.0 4.0-4.11
30
25
10
Table 2
(a) Find the mean length of the sample of iron rods.
(b) Construct a histogram according to the above frequency
chstribution.
(c) It is intended to remove the longest 30% of rods. From your histogram, determine the shortest length of the iron rods that should be removed.
(d) If there are totally 150,000 iron rods in the wharehouse, estimate the total number of rods which are, Jonger than the mean length.
3. Table 3 shows the distribution of 100 candidates in a mathematics best and its data is plotted in the accompanying graph (see figure 1)
umber of Dandi.iates
jwan score Bbove or equal to)
11:07
50-
67
.55
5. (a) In
the first Mathematics test, the mear and standard deviation were 60 and 8 respectively.
The results of six students are shown in table 6 below.
15
Name of student, Mark Deviation from mean Standard score
John
64
Mary
68
Paul
52
100
90-
David
56
tol
80
Joan
76
Susanna
72
Tabic 6
Number of candidates
(who score above or equal
60-
40-
301
20
10.
Complete the table.
(b) In the second Mathematics test to the same class a few weeks later, the mean was 45 and the standard deviation 6. The results of the six students are shown in table 7 below.
Name of student Mark Deviation from mean Standard score
John
54
Mary
48
Paul
39
David
45
60
$usanna
51
Table 7
Marks
Number of candidates who score?
above or equal to this markety
...ก
10
20
30
36
90
80
Complete the table.
(c) i. Which one of the six students improved most?
ij. Which studert came down most in the second test? iii. Which student was most consistent in the two tests?
ران
60
50
32
60
12
Solutions to Exercise 25
70
1
1. (a) Number
1
التور
0
Table 3.
Probability
The required probability
- Gaga - GRD GOGO
77
(b). The required probability:
+
Marks
10
20
30
40
10 20
30
50 60 70. 80
Marks
(Ans.}
Number of students with marks below this mark
A
Cumulative Frequency
120-
10
10
1001
80-
G04
{Ans. 1
40f
PUBLIC
(c) The probability
(b)
(Ans)
14
30
48
78
110
120
20
30
40
50
60 Marks
From the graph, 66 students (55% of the students) with marks less than 36, therefore the pass mark is 36.
ii. From the graph, 39 students with marks. less than 25,
therefore
the pass percentage
50
At Mrks
Figure 1
(a) fill in table 1 below
100
Range of marks
Number of candidates who score.x
0 < x < 10
10 < x < 20 20 < x < 30 30-6 x < 40
40 x 50
50 x 60
·60 X x < 70
70 < x < 80
120-39
* 100% 120
= 67.5%
(Ans.
90 iii. x 120 = 114
100
2. (a) The wean length
3x3,55+7x3.65+15x3.75+30x3.85+25x3.95+10x4.05+8x4.15+2x4.25 5. (a)
3:889 cm
(b)
(Ans.)
Table 4.
Frequency
(b) If 25% of the candidates failed in the test, estimate the
pass mark of the test.
30
(c) If a candidate is picked at random from those who pass the test, what is the probability that his score is less than 56?.
20-
4. The following graph shows the distribution of 120 candidates in
an examination.
10+
(Ans.)
正確工有背高明指正 上述兩姓混音,認就所知奉告。是否
敦到獎
From the graph, 114 students with marks less than 54, therefore, the range of grade. 'A', is 54 $0. (excluding 54)
Name of student Mark Deviation from mean Standard score
(D)
John
64
4
Mary
be
Paul
52
-8
-1
David
56
-4
-0.5
Joan
Susanna
76
16.
2
72
12
1.5
Table 1
Name of student Mark Deviation from mean Standard scorel
المخدا
張庭
John
54
9
1.5
Mary
48
3
0.5
Cumulative frequency
3.5 3.5 3.7 3.8 3.9 4.0 4.1 4.2 4.3
3.56
Paul
39
-6.
-1
100-
80
60
404
20-
(c) The number of rods should be removed - 3 x 100 = 30
David
45
0
0
From the graph, the shortest length of the iron rods that should be removed is 3.95 cm.
[Ans.)
Joan
60
15
2.5
Susannia
52
1.167
(d) 48 iron rods are longer than the mean length among 100
rods.
48
Table 2
x 160000
= 76800
Ans.)
20
30
30
50
60. Marks
Figure 2
26800 rods are longer than the mean length among 160000 rods.
(c) i.John improved most for his standard score increases most. 13 Mary came down moss for her standard score decreases
most.
iii. Paul, for his standard score is neither increased nor
decreased.
圖文傳眞
熱線電話 熱誠服務 •
5462583
5464459
5594238
每日下午五點半截稿
(廣分)
靄報日僑華
(告類)
(刊明)
(出天) ]]]
今日(廣分)
若不持 香處突ㄝ
那個結製
(告類)
個是大家