Download Example I A weight has a measurement error, E, that can be

Example I
measures at least ±1 gram wrong?
A weight has a measurement error, E,
that can be described by a standard
normal disrtribution, i.e.
E ∼ N (0, 12)
that is, mean µ = 0 and standard deviation σ = 1 gram.
We now measure the weight of a single
piece
a) What is the probability that the
weight measures at least 2 grams too
little?
b) What is the probability that the weight
measures at least 2 grams too much?
c) What is the probability that the weight
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Example II
Example III
It is assumed that among a group af elementary school teachers, the salary distribution can be described as a normal
distribution with mean µ = 280.000
and standard deviation σ = 10.000.
It is assumed that among a group af elementary school teachers, the salary distribution can be described as a normal
distribution with mean µ = 290.000
and standard deviation σ = 4.000.
a) What is the probability that a randomly selected teacher earns mor than
300.000?
a) What is the probability that a randomly selected teacher earns mor than
300.000?
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Example IV
Example V
It is assumed that among a group af elementary school teachers, the salary distribution can be described as a normal
distribution with mean µ = 290.000
and standard deviation σ = 4.000.
In a dose-response experiment with 80
rats, it is assumed that the probability that a rat survives the experiment is
p = 0.5.
a) Give the salary interval that covers
95% of all teachers salary
a) What is the probability that at most
30 rats die in the experiment?
b) What is the probability that between
38 and 42 rats die in the experiment?
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Example VI
Example VII
The particle size (µm) in a compoundi
is assumed to follow a Log-normal distribution with α = 0.73 and β = 0.44.
The particle size (µm) in a compoundi
is assumed to follow a Log-normal distribution. We have the oberservations:
2.2 3.4 1.6 0.8 2.7 3.3 1.6 2.8
1.9
What is the proportion of particles
with a size in the interval [2; 3]
We take the logarithm of the data and
achieve:
0.8 1.2 0.5 -0.2 1.0 1.2 0.5 1.0
0.6
from which we get: x̄ = 0.733 and s =
0.44.
What is the proportion of particles
with a size in the interval [2; 3]
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Example VIII
Students in a course arrive to a lecture
between 7.45 and 8.15. It is assumed
that the arival times can be described
by a uniform distribution.
What is the probability that a randomly selected student arrives between
8.05 and 8.15?
What is the probability that a randomly selected student arrives after
8.15?
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