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Given x and y as species whose interaction is governed by
x
0 = x (( 20 0 x + 2y)
y
0 = y (( 50 + x x y),
(i) Identify the type of interaction represented by this system.
(ii) Determine the equilibrium points of this model and state the possible outcomes of
this interaction.
(iii) Linearise the system around each equilibrium point and hence discuss the nature of
the stability of each equilibrium point.
(iv) Sketch the phase portrait of the above system.
Solve, using the method of separation of variables, the PDE
∂u
∂t +
∂u
∂x + 2e
tu = 0
The average time it takes a group of Senior High School student to complete a certain examination is 48.2 minutes. The standard deviation is 7 minutes. Assume that the variable is normally distributed. If 20 randomly selected SHS student take the examination, what is the probability that the mean time it takes the group to complete the test will be more than 45 minutes?
An insurance salesman sells policies to 5 men, all of identical age in good health. According to
the actuarial tables the probability that a man of this particular age will be alive 30 years hence is
2 /3 . Find the probability that in 30 years
(i) All men will be alive
(ii) At least 3 men will be alive
(iii) Only two men will be alive
(iv) At least 1 man will be alive
A pottery produces royal souvenir mugs. It is known that 6% are defective. If 20 mugs
are selected at random. Find the probability that the sample contains less than 5
defective mugs.
The marks of 500 candidates in an examination are normally distributed with a mean of 45
marks and a standard deviation of 20 marks.
(a) Given that the pass mark is 41, estimate the number of candidates who passed the
examination
(b) If 5% of the candidates obtain a distinction by scoring 𝑥 marks or more, estimate the value
of 𝑥.
The heights of female students at a particular University are distributed with mean of 169 cm
and a standard deviation of 9 cm.
(a) Given that 80% of these female students have a height less than b cm, find the of b.
(b) Given than 60% of these female students have height greater than 5 cm, find the value of s.
Each of 39 of my friends has either a dog a cat or a rabbit each of 24 of them has a dog each of 17 gas a cat and each of 16 has a rabbit the number having both a dog and a cat is one more than the number having both a cat and a rabbit while 2of them have all the three how many of my friends have both a rabbit and cat
The height of students at a university taking introduction to probability are nomally distributed with mean height of 50 cm and standard deviation 10 cm. Find the probability that the height of a randomly selected standard is
(a) shorter than Wye
(b) within 5 cm of the mean
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