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Mathematics
UTME / JAMB 2008
Statistics and Probability
Solution
The probability of picking a letter T from the word OBSTRUCTION is?
A
1/11
B
2/11
C
3/11
D
4/11
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
OBSTRUCTION
Total possible outcome = 11
Number of chance of getting T = 2
P(picking T) = 2/11
Source: Myschool Past Questions Archive (Record #9301)
Mathematics
UTME / JAMB 2008
Statistics and Probability
Diagram
Solution
The result of rolling a fair die 150 times is as summarized in the table above. What is the probability of obtaining a 5?
Attached Figure / Diagram
A
3/10
B
1/5
C
1/6
D
1/10
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Total possible outcome
12+18+x+30+2x+45 = 105+3x
∴105+3x = 150
3x = 150-105
3x = 45
x = 15
P(obtaining 5) = \(\frac{2x}{(105+3x)}\) But x= 15
=\(\frac{2(15)}{(105+3(15))}\)
=\(\frac{30}{(105+45)}\)
=\(\frac{30}{150}\)
=\(\frac{1}{5}\)
Source: Myschool Past Questions Archive (Record #9302)
Mathematics
WAEC / WASSCE 2008
Statistics and Probability
Solution
Find the mean deviation of these numbers 10, 12, 14, 15, 17, 19.
A
2.5
B
2.6
C
2.7
D
2.8
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\begin{array}{c|c} x & d = x - \bar{x} & |d| \\ \hline 10 & -4.5 & 4.5 \\ 12 & -2.5 & 2.5\\ 14 & -0.5 & 0.5\\ 15 & 0.5 & 0.5\\ 17 & 2.5 & 2.5\\ 19 & 4.5 & 4.5\\ \hline \sum x = 87 & & \sum|d| = 15\end{array}\)
\(\bar{x} = \frac{\sum x}{n}\)
= \(\frac{87}{6}\)
= 14.5
Source: Myschool Past Questions Archive (Record #36401)
Mathematics
NECO SSCE 2008
Statistics and Probability
Solution
Twenty girls and y boys sat on an examination. The mean marks obtained by the girls and boys were 52 and 57 respectively. if the total score for both girls and boys was 2750, find y.
A
51
B
48
C
30
D
25
E
18
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Let the total score for the girls and the boys be A and B respectively.
\(\frac{A}{20} = 52 \implies A = 52 \times 20\)
A = 1040
\(\frac{B}{y} = 57 \implies B = 57y\)
1040 + 57y = 2750
57y = 2750 - 1040
57y = 1710
y = \(\frac{1710}{57}\)
y = 30
Source: Myschool Past Questions Archive (Record #42495)
Mathematics
NECO SSCE 2008
Statistics and Probability
Find the mean deviation of 20, 25, 21, 27, 28, 29, to the nearest whole number
A
2
B
3
C
4
D
5
E
6
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #42516)
Mathematics
NECO SSCE 2008
Statistics and Probability
The ages of Abu, Segun, Kofi and Funmi are 17 years, (2x -13) years, 14 years and 16 years respectively. What is the value of x if their mean ages is 17.5 years?
A
18
B
23
C
25
D
36
E
70
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option A.
Source: Myschool Past Questions Archive (Record #42546)
Mathematics
NECO SSCE 2008
Statistics and Probability
The median of a distribution can be estimated from
A
Barchart
B
Cumulative frequency curve
C
Frequency polygon
D
Pictorial
E
Pie chart
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #42660)
Mathematics
NECO SSCE 2008
Statistics and Probability
Solution
The graph of cumulative frequency distribution is known as
A
an ogive
B
a histogram
C
a frequency polygon
D
relative frequency
E
none
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
An ogive is a graph that shows a cumulative frequency distribution, plotting cumulative frequencies against upper class boundaries to form an "S"-shaped curve.
Source: Myschool Past Questions Archive (Record #42663)
Mathematics
UTME / JAMB 2007
Statistics and Probability
Solution
If 5, 8, 6 and 2 occur with frequencies 3, 2, 4 and 1 respectively. Find the product of the modal and the median number
A
36
B
48
C
30
D
40
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Arrange in ascending order
2, 5, 5, 5, 6, 6, 6, 6, 8, 8
Position of median = N/2 = 10/2 = 5th and 6th
∴Median = (6+6) / 2 = 12/2 = 6
Mode the item that repeats itself most = 6
∴Product of modal and median number = 6 x 6 = 36
Source: Myschool Past Questions Archive (Record #9083)
Mathematics
UTME / JAMB 2007
Statistics and Probability
Solution
In a basket, there are 6 grapes, 11 bananas and 13 oranges. If one fruit is chosen at random. What is the probability that the fruit is either a grape or a banana
A
6/30
B
5/30
C
17/30
D
11/30
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Number of grapes = 6
Number of banana = 11
Number of oranges = 13
Total = 30
P(Grape) = 6/30, P(Banana) = 11/30
P(Orange) = 13/30
∴P(Either grape or banana) = 6/30 + 11/30
= 17/30
Source: Myschool Past Questions Archive (Record #9107)
Mathematics
UTME / JAMB 2007
Statistics and Probability
Diagram
Solution
The table above shows the number of pupils in each age group in a class. What is the probability that a pupil chosen at random is at least 11 years old?
Attached Figure / Diagram
A
27/40
B
17/20
C
3/30
D
33/40
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
P(At least 11 yrs) = P(11yrs) + P(12yrs)
= \(\frac{27}{40}\) + \(\frac{7}{40}\)
= \(\frac{34}{40}\)
= \(\frac{17}{20}\)
Source: Myschool Past Questions Archive (Record #9152)
Mathematics
UTME / JAMB 2007
Statistics and Probability
Solution
What is the mean deviation of 3, 5, 8, 11, 12 and 21?
A
4.7
B
60
C
3.7
D
10
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Mean \(= \bar{x} = \frac{60}{6} = 10\)
mean deviation \(= \frac{\sum|x-\bar{x}|}{n} = \frac{28}{6}\)
= 4.7
Source: Myschool Past Questions Archive (Record #9218)
Mathematics
UTME / JAMB 2007
Statistics and Probability
Solution
Marks
3
4
5
6
7
8
Frequency
5
(y - 1)
y
9
4
1
The table above gives the frequency distribution of marks obtained by a group of students in a test. If the total mark scored is 200, calculate the value of y
A
15
B
13
C
11
D
8
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Total mark scored = 200
∴200 = 15 + 4y - 4 + 5y + 54 + 28 + 8
200 = 9y + 101
200 - 101 = 9y
99 = 9y
∴y = 11
Source: Myschool Past Questions Archive (Record #9219)
Mathematics
WAEC / WASSCE 2007
Statistics and Probability
The table above gives the distribution of the marks of a number of students in a test.
\(\begin{array}{c|c} Mark &1 & 2 & 3 & 4 & 5 & 6 \\ \hline Frequency & 5 & 3 & 6 & 4 & 2 & 5\end{array}\), find the mode of the distribution.
A
2
B
3
C
5
D
6
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #36273)
Mathematics
WAEC / WASSCE 2007
Statistics and Probability
Solution
If the probability of an event occurring is x, what is the probability of the event not occurring?
A
1 - x
B
x - 1
C
0
D
\(\frac{1}{x}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
If p is the probability of an event happening(occurring) and the probability of an event not occurring is p1 then p + p1 = 1
p1 = 1 - p
x1 = 1 - x
Source: Myschool Past Questions Archive (Record #36275)