IEE 380 Exam 1 Questions and Correct Answers
The probability a lab specimen contains high levels of contamination is 0.15. A group of
3 independent samples are checked.
What is the probability that exactly one sample contains high levels of contamination?
0.3251
P(H1 n H2' n H3') + P(H1' n H2 n H3') + P(H1' n H2' n H3)
In Siberia there is a probability of 0.50 that a person is wearing a fur coat, in Urals
there is a probability of 0.70 that a person will be wearing a fur coat. There is a
probability of .60 that you are in Siberia and a probability of 0.40 that you are in Urals.
What is the probability that a person is not wearing a fur coat?
N = Not wearing a fur coat
S = In Siberia
U = In Urals
P(N) = P(N|S) x P(S) + P(N|U) x P(U) = 0.42
What is another term for mean?
Expected value
For the case of the thin copper wire, suppose that the number of flaws, X, follows a
Poisson distribution with a rate of 2.3 flaws per mm. A 2mm piece of wire is defective if
, it contains at least 1 flaw. What is the probability there are no defective pieces of wire if
we sample fifty 2mm pieces?
Lambda = 2.3
T=2
P(X=0) = possionpdf(2.3(2), 0) = 0.1005
P(Y=50) = binompdf(50, 0.1005, 50) = 0
Therefore the probability is 0
Let the continuous random variable X denote the current measured in a thin copper
wire in milliamperes (mA). Assume that the range of X is 4.9 <= x <= 5.1 and f(x) = 5.
What is the probability that a current is less than 5mA?
Continuous so P(X < 5) = integral from 4.9 to 5.0 of 5dx = 0.50
The time until a chemical reaction is complete in ms is approximated by this cumulative
distribution function:
F(x) = 0 for x < 0 and 1-e^(-0.01x) for 0 <= x
What proportion of reactions is complete within 200ms?
P(X < 200) = P (X <= 200) = F(200) = 1-e^(-0.01(200)) = 0.8647
The random variable X has a continuous uniform distribution on [4.9, 5.1].
The pdf of X is f(x) = 5, 4.9 <= x <= 5.
The probability a lab specimen contains high levels of contamination is 0.15. A group of
3 independent samples are checked.
What is the probability that exactly one sample contains high levels of contamination?
0.3251
P(H1 n H2' n H3') + P(H1' n H2 n H3') + P(H1' n H2' n H3)
In Siberia there is a probability of 0.50 that a person is wearing a fur coat, in Urals
there is a probability of 0.70 that a person will be wearing a fur coat. There is a
probability of .60 that you are in Siberia and a probability of 0.40 that you are in Urals.
What is the probability that a person is not wearing a fur coat?
N = Not wearing a fur coat
S = In Siberia
U = In Urals
P(N) = P(N|S) x P(S) + P(N|U) x P(U) = 0.42
What is another term for mean?
Expected value
For the case of the thin copper wire, suppose that the number of flaws, X, follows a
Poisson distribution with a rate of 2.3 flaws per mm. A 2mm piece of wire is defective if
, it contains at least 1 flaw. What is the probability there are no defective pieces of wire if
we sample fifty 2mm pieces?
Lambda = 2.3
T=2
P(X=0) = possionpdf(2.3(2), 0) = 0.1005
P(Y=50) = binompdf(50, 0.1005, 50) = 0
Therefore the probability is 0
Let the continuous random variable X denote the current measured in a thin copper
wire in milliamperes (mA). Assume that the range of X is 4.9 <= x <= 5.1 and f(x) = 5.
What is the probability that a current is less than 5mA?
Continuous so P(X < 5) = integral from 4.9 to 5.0 of 5dx = 0.50
The time until a chemical reaction is complete in ms is approximated by this cumulative
distribution function:
F(x) = 0 for x < 0 and 1-e^(-0.01x) for 0 <= x
What proportion of reactions is complete within 200ms?
P(X < 200) = P (X <= 200) = F(200) = 1-e^(-0.01(200)) = 0.8647
The random variable X has a continuous uniform distribution on [4.9, 5.1].
The pdf of X is f(x) = 5, 4.9 <= x <= 5.
