( 27 )育教 日八初月二年未辛夏
1991 中學會考預習專欄
明德出版社,
MILL & DALE PRESS
Mathematics (25)
郭日僑墨
日八初」
六期星
日三廿月三(一九九一)年十八國民藥中
(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
0x < 10
4
10 < x < 20
6
10
20
30
40
20 x 30
30 X 40
40 x 50-
50 x 60
10
20
28
50 60
Table 5
60x70
70 < x < 80
(b) 25% of the candidates failed in the test 75 candidates above
or equal to 32.5
20
8
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務間 5-
鸝 鐧:每日上午十時至下午五時半
Exercise 25: Experimental probability and statistics
H. K. Lo
(b) Determine, from the graph,
i. the pass mark, if the pass percentage is 45% ii. the pass percentage if the pass mark is 25 iit. If 95% of the students got grades lower than 'A', find
the range of the grade.
The frequencies of the Is. (a) In the 1. A loaded die is thrown 1000 times.
numbers which turn up are given in the following table
.. pass mark = 32.5
(Ans.)
(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
first Mathematics test, the mean and standard deviation were 60 and 8 respectively. The results of six students are, shown in table 6 below.
Number
Frequency
1
200
2.
3
5
6
Name of student Mark Deviation from mean Standard score
100
200
100
100
300
John
64
Table 1
Mary
68
Paul
52
David
56
Joan
76
Susanna,
72
Table 6
(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
both number's 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 both even?
2. The lengths of a random sample of 100 tron rods from a wharehouse
are measured and the frequency distribution is as follows
Length (in cm)
Frequency
3.5-3.6 3.6-3.7 3.7-3.8 3.8-3.93.9-4.04.0-4.1 4.1-4.2 4.2-4.3
3
7
15.
30
25
10
a
2
Table 2
(a) Pind the mean length of the sample of iron rods.
(b) Construct a histogram according to the above frequency
distribution. E
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. results of the six students are shown in table 7 below..
Name of student Mark Deviation from mean Standard score'
John
54
[Mary
48
(c) It is intended to remove the longest 30% of rods. histogram, determine the shortest length of the that should be removed.
From your
Paul
39
iron rods.
David
45
Joan
60
51
7
Compete the table.
The
Number of candidates
(who score above or equal to) ·
100
.90
60-
50
30
20
10
(d) If there are totally 160,000 iron rods in the wharehouse, estimate the total number of rads which are longer than the mean length.
3. Table 3 shows the distribution of 100 candidates in a mathematics.
test and its data is plotted in the accompanying grap figure 1)
Marks
Number of candidates who score
above or equal to this mark
圖
4. (a)
Marks
10
20
30
40
1. Which one of the six students. improved most?
ii. Which student came down most in the second test?
iii. Which student was most consistent in the two tests
10 20 30
Marks
(Ans.)
Number of students with marks below this mark
圖文
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1,00
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50
60
70
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Table 3.
(a) Fill in table 4. below
100
.96
95
80
60
Solutions to Exercise 25.
32
1. (a) Number
1
2:
3
4
5
120-
Probability
ड
10
10
The required probability
(8) (3) + (78) (8) + (7}}(77)
(b) The required probability
(금) () + (구)(금)
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(c)
40
50
60
70
BO Marks
Figure 1
100
Range of marks
Number of candidates who score x
0 $ x ≤ 10.
2. (a). The mean length
10 < x < 20
30
20 < x <.30
x 40
40 < x < 50
50 x 60
60 < x < 70
70 < x < 80
Table 4
(b) If 25% of the candidates failed in the test, estimate the
pass mark of the test.
(Ans.)
LIB
(b) i.
Cumulative Frequency
14
30
48
78.
110
120
10.
20.
30
40
50
60 Marks
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From th graph, 66 students (55% of the students) with marks less than 36, therefore the pass mark is 36.
it. From the graph, 39 students with marks less than 25,
therefore
(封口機 縮壊)(
362814
3332035
the pass percentage =
120-39
120 * 100%
67.5%
95
(Ans.)
iii.20 x 120 = 114
(Ans.)
From the graph, 114 students with marks less than 54, therefore, the range of grade 'A' is 54 - 60. (excluding 54)
3x3.55+7x3.65+15x3.75+30x3.85+25x3.95+10x4.05+8x4.15+2x4.25 5. (a) Mame of student Mark Deviation from mean Standard score
= 3.889 cm
(b)
Frequency
30-
(c) If a candidate is picked at random from those who pass the test, what is the probability that his score is Tess than 56?
201
100
(Ans.)
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John
64
4
0.5
Mary
58
8
1
Paul
52
-8
-1
David
56
~4
-0.5
78
Joan
Susanna
76
16
72
12
2
1.5
敦道 65g
Table 1
10
4. The following graph shows the distribution of 120 candidates in
an examination.
(b).
Name of student Mark Deviation from mean Standard score
Cumulative frequency
10-
80
AO
40
John
54
g
1.5
3.5 3.6 3.7 3.8 3.9 4.0 4.1 4,2 4.3
Mary
48
3
0.5
3.96
Paul
39
-6
-1
x. 100 = 30 (c) The number of rods should be removed = 100
From the graph, the shortest length of the iron rods that {Ans.) should be removed is 3.96 cm.
30
David
45
0
0
Joan
60
15
2.5
Susanno
52
7
1.167
Table 2
rods.
48
20
% 160000
100
0
= 76800
(Ans.)
10
20
30
40
50
60 Marks
Figure 2
76800 rods are longer than the mean length among 160000 ruds.
(d) 46 iron rods are longer than the mean length among 100
(c) i. John improved most for his standard score increases most.
ii. Mary came down most for her standard score decreases
post.
iii. Paul, for his standard score is neither increased nor
decreased.
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