1. In factory,
the number of accidents occurring in a week follows a poison distribution with
a
mean of 4.2. Find the probability that
a) Exactly
5 accidents will occur in a particular week.
(2
marks)
b) Less
than 12 accidents will occur in a particular fortnight
(3 marks)
2. In
an examination, a total of 15000 students sat for a Mathematics paper. The
marks obtained by the students are normally distributed with a mean of 61 marks
and a standard deviation of 10 marks.
a) Given
that a distinction is given for a student who obtained 85 marks or more,
estimate the number of students who obtained distinctions in the Mathematics
paper.
(5 marks)
b) If
90% of the students who sat for the Mathematics paper in the examination
passed, estimate the minimum mark to pass.
(5 marks)
c) If a
student is picked at random, find the probability that the student obtained a
mark between 55 and 74 in the Mathematics paper.
(5 marks)
3. In a
shooting practice, the probability that a shooter hits a target is 0.45. If
shooter attempts 6 shots, calculate the probability that
a) Exactly
5 shots hit the target
(3
marks)
b) At
most 3 shots hit the target
(3
marks)
4.The
probability density function of a continuous random variable X is given by where k is constant.
a) Determine
the value of k
b) Find
the cumulative distribution function of X, F(X)
c) Calculate
i.
Var(X)
ii.
Var(3X – 5)
iii.
P( |X| > 2)
5. The
probability distribution function of a discrete random variable X is given by
a) Show
that k = 4/15
b) Find
Var (X)
ANSWER :
1 a) 0.1633
b) 0.8571
2 a) 123
b) 48.2
c) 0.6289
3 a) 0.0609
b) 0.7447
4
5 a) k
= 4/15
b) 14/9
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