Question
In: Statistics and Probability
Let X represent the full height of a certain species of tree. Assume that X has...
Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with a mean of 77 ft and a standard deviation of 3.5 ft. A tree of this type grows in my backyard, and it stands 65.8 feet tall.
Find the probability that the height of a randomly selected tree is as tall as mine or shorter.
P(X<65.8)=
My neighbor also has a tree of this type growing in her backyard, but hers stands 80.2 feet tall. Find the probability that the full height of a randomly selected tree is at least as tall as hers.
P(X>80.2) =
Enter your answers as decimals accurate to 3 decimal places.
Solutions
orchestra answered 2 years agoRelated Solutions
Once an individual has been infected with a certain disease, let X represent the time (days)...
Once an individual has been infected with a certain disease, let
X represent the time (days) that elapses before the individual
becomes infectious. An article proposes a Weibull distribution with
α = 2.6, β = 1.1, and γ = 0.5. [Hint: The two-parameter Weibull
distribution can be generalized by introducing a third parameter γ,
called a threshold or location parameter: replace x in the equation
below, f(x; α, β) = α βα xα − 1e−(x/β)α x ≥ 0 0 x...
Once an individual has been infected with a certain disease, let X represent the time (days)...
Once an individual has been infected with a certain disease, let
X represent the time (days) that elapses before the individual
becomes infectious. The article “The Probability of Containment for
Multitype Branching Process Models for Emerging Epidemics” (J. of
Applied Probability, 2011: 173-188) proposes a Weibull distribution
with alpha = 2.2, beta = 1.1, and gamma = 0.5
a. Calculate P(1 < X < 2).
b. Calculate P(X > 1.5).
c. What is the 90th percentile of the distribution?
d....
Let X be the height of a student to be randomly selected at the University. Assume...
Let X be the height of a student to be randomly selected at the
University. Assume (for the purpose of modeling) that X has the
normal distribution with a mean of 68 inches and a standard
deviation of 4.9 inches.
a.) What is the probability a randomly selected student is
shorter than 65 inches?
b.) What is the probability a randomly selected student is
taller than 73 inches?
c.) What is the probability a randomly selected student's height
falls within...
Let X be the height of a student to be randomly selected at the University. Assume...
Let X be the height of a student to be randomly selected at the
University. Assume (for the purpose of modeling) that X has the
normal distribution with a mean of 68 inches and a standard
deviation of 4.9 inches.
a.) What is the probability a randomly selected student is
shorter than 65 inches?
b.) What is the probability a randomly selected student is
taller than 73 inches?
c.) What is the probability a randomly selected student's height
falls within...
6.2% of cable boxes of a certain type are defective. Let the random variable X represent...
6.2% of cable boxes of a certain type are defective. Let the
random variable X represent the number of defective cable boxes
among 200 randomly selected boxes of this type. Suppose you wish to
find the probability that X is equal to 8.
(i) Does the random variable X have a binomial or a Poisson
distribution? How can you tell? (ii) If X has a binomial
distribution, would it be reasonable to use the Poisson
approximation? If not, why not?
Measuring the height of a particular species of tree is very difficult because these trees grow...
Measuring the height of a particular species of tree is very
difficult because these trees grow to tremendous heights. People
familiar with these trees understand that the height of a tree of
this species is related to other characteristics of the tree,
including the diameter of the tree at the breast height of a
person. The accompanying data represent the height (in feet) and
diameter (in inches) at the breast height of a person for a sample
of 21 trees...
Measuring the height of a particular species of tree is very difficult because these trees grow...
Measuring the height of a particular species of tree is very
difficult because these trees grow to tremendous heights. People
familiar with these trees understand that the height of a tree of
this species is related to other characteristics of the tree,
including the diameter of the tree at the breast height of a
person. The accompanying data represent the height (in feet) and
diameter (in inches) at the breast height of a person for a sample
of 21 trees...
Measuring the height of a particular species of tree is very difficult because these trees grow...
Measuring the height of a particular species of tree is very
difficult because these trees grow to tremendous heights. People
familiar with these trees understand that the height of a tree of
this species is related to other characteristics of the tree,
including the diameter of the tree at the breast height of a
person. The accompanying data represent the height (in feet) and
diameter (in inches) at the breast height of a person for a sample
of 21 trees...
Measuring the height of a particular species of tree is very difficult because these trees grow...
Measuring the height of a particular species of tree is very
difficult because these trees grow to tremendous heights. People
familiar with these trees understand that the height of a tree of
this species is related to other characteristics of the tree,
including the diameter of the tree at the breast height of a
person. The accompanying data represent the height (in feet) and
diameter (in inches) at the breast height of a person for a sample
of 21 trees...
Let X represent the weight of the students at a university. Suppose X has a mean...
Let X represent the weight of the students at a university.
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Among 100 such randomly selected students from this university,
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sample (X100) lies between
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(b) greater than 76 kg
(c) less than 73 kg
Assume that the sample size(N) is large enough for the CLT
(Central Limit Theorem) to...
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