Search
In a Competitive examination of 5000 students, the marks of the examinees in statistics were found to be distributed normally with mean 45 and standard deviations 14.
Determine the number of examinees whose marks, out of 100 were;
(i) Less than 30. 2MKS
(ii) Between 30 and 70. 2MKS
(iii) Between 60 and 80. 2MKS
(iv) More than 60. 2MKS
(v) More than 40 2MKS
Find the corresponding area between z = 0 and each of the following.
1. Z = 0,85
2. Z = 1.27
3. z = 2.86
4. Z = -1.05
5. Z = -2.96
Find a basis and the dimension of the subspace W of ℝ^3 where W = {( x, y, z ) ∈ ℝ^3 ∶ x + y + z = 0 }.
Express each of these mathematical statements using predicates, quantifiers, logical connectives, and mathematical operators.
a) The product of two negative real numbers is positive.
b) The difference of a real number and itself is zero.
c) Every positive real number has exactly two square roots.
d) A negative real number does not have a square root that is a real number. e) Every non-zero real number has a unique reciprocal.
Determine the subspace of ℝ^3 spanned by the vectors α = 1, 2, 3 , β = 3, 1, 0 . Examine whether
γ = 2, 1, 3 , δ = (−1, 3, 6) are in the subspace or not.
A university has analyzed the results of 1,000 students after the first year examinations. The result of the analysis is summarized below
Types of sponsorship
Examination results
Government
Private
Church
Students who were to be discontinued
155
150
105
Students who passed the examination
180
195
170
Students who were to sit for a supplementary paper
20
5
20
Required
The probability that a student was discontinued or was required to sit for a supplementary paper (1mark)
The probability that a student was a government sponsored (1mark)
The probability that a privately sponsored student passed the examination (2marks)
In a Competitive examination of 5000 students, the marks of the examinees in statistics were found to be distributed normally with mean 45 and standard deviations 14.
Determine the number of examinees whose marks, out of 100 were;
(i) Less than 30. 2MKS
(ii) Between 30 and 70. 2MKS
(iii) Between 60 and 80. 2MKS
(iv) More than 60. 2MKS
(v) More than 40 2MKS
Translate each of these nested quantifications into an English statement that expresses a mathematical fact. The domain in each case consists of all real numbers.
a) ∃x ∀y(x + y = y)
b) ∀x ∀y (((x ≥ 0) ∧ (y < 0)) → (x − y > 0))
c) ∃x ∃y(((x ≤ 0) ∧ (y ≤ 0)) ∧ (x − y > 0))
d) ∀x ∀y((x ≠ 0) ∧ (y ≠ 0) ↔ (xy ≠ 0))
Apply definition of antiderivative and find area under the curve of f(x) = x^1/2 between x=0 and
x=1
Find absolute maximum and minimum of the function f(x) = 2x^2- 5 in [-1, 2].
