Question

Suppose the proportion *X* of surface area in a randomly
selected quadrat that is covered by a certain plant has a standard
beta distribution with *α* = 4 and *β* = 2.

(a) Compute *E*(*X*) and *V*(*X*).
(Round your answers to four decimal places.)

E(X) = |
0.6667 |

V(X) = |
0.0317 |

(b) Compute *P*(*X* ≤ 0.2). (Round your answer to
four decimal places.)

(c) Compute *P*(0.2 ≤ *X* ≤ 0.5). (Round your answer
to four decimal places.)

(d) What is the expected proportion of the sampling region not
covered by the plant? (Round your answer to four decimal
places.)

Answer #1

Suppose the proportion X of surface area in a randomly
selected quadrat that is covered by a certain plant has a standard
beta distribution with α = 5 and β = 4.
(a) Compute E(X) and V(X).
(Round your answers to four decimal places.)
E(X) =
V(X) =
(b) Compute P(X ≤ 0.4). (Round your answer to
four decimal places.)
(c) Compute P(0.4 ≤ X ≤ 0.8). (Round your answer
to four decimal places.)
(d) What is the expected proportion...

Suppose the proportion X of surface area in a randomly
selected quadrat that is covered by a certain plant has a standard
beta distribution with α = 5 and β = 2.
(a) Compute E(X) and V(X).
(Round your answers to four decimal places.)
E(X) =
V(X) =
(b) Compute P(X ≤ 0.4). (Round your answer to
four decimal places.)
(c) Compute P(0.4 ≤ X ≤ 0.8). (Round your answer
to four decimal places.)
(d) What is the expected proportion...

(a) Approximate the area of the region beneath the graph of
f(x) =
e−x2,
from x = −1 to x = 1 using (i)
four left rectangles, (ii) four right rectangles, and (iii) four
midpoint rectangles (answer with 3 decimal points).
(b) The actual area, to nine decimal places, of the region
beneath the graph of f(x) =
e−x2 is 1.493648266. Which
of the approximations found in part (a) is the most accurate?

X ~ N(70, 9). Suppose that you form random samples of 25 from
this distribution. Let X be the random variable of averages. Let ΣX
be the random variable of sums.
B) Give the distribution of
X.
(Enter an exact number as an integer, fraction, or decimal.)
C)Sketch the graph, shade the region, label and scale the
horizontal axis for
X,
and find the probability. (Round your answer to four decimal
places.)
P(X < 70) =
D)Find the 20th percentile....

The following is based on information from The Wolf in the
Southwest: The Making of an Endangered Species, by David E. Brown
(University of Arizona Press). Before 1918, the proportion of
female wolves in the general population of all southwestern wolves
was about 50%. However, after 1918, southwestern cattle ranchers
began a widespread effort to destroy wolves. In a recent sample of
37 wolves, there were only 11 females. One theory is that male
wolves tend to return sooner than...

The following is based on information from The Wolf in the
Southwest: The Making of an Endangered Species, by David E. Brown
(University of Arizona Press). Before 1918, the proportion of
female wolves in the general population of all southwestern wolves
was about 50%. However, after 1918, southwestern cattle ranchers
began a widespread effort to destroy wolves. In a recent sample of
37 wolves, there were only 11 females. One theory is that male
wolves tend to return sooner than...

The following is based on information from The Wolf in the
Southwest: The Making of an Endangered Species, by David E.
Brown (University of Arizona Press). Before 1918, the proportion of
female wolves in the general population of all southwestern wolves
was about 50%. However, after 1918, southwestern cattle ranchers
began a widespread effort to destroy wolves. In a recent sample of
37 wolves, there were only 11 females. One theory is that male
wolves tend to return sooner than...

X ~ N(50, 9). Suppose that you form random
samples of 25 from this distribution.
Let X be the random variable of averages.
Part (a)
Sketch the distributions of X and X-bar on the
same graph.
Part (b)
Give the distribution of X-bar.
(Enter an exact number as an integer, fraction, or decimal.)
X ~
,
Part (c)
Sketch the graph, shade the region, label and scale the horizontal
axis for
X-bar, and find the probability. (Round your answer to...

(a) Estimate the area under the graph of f(x) = 2/x from x = 1
to x = 2 using four approximating rectangles and right endpoints.
(Round your answer to four decimal places.)
(b) Repeat part (a) using left endpoints. (Round your answer to
four decimal places.)

Suppose that a random sample of size 64 is to be selected from a
population with mean 40 and standard deviation 5.
(a) What are the mean and standard deviation of the sampling
distribution?
μx =
σx =
(b) What is the approximate probability that x will be
within 0.4 of the population mean μ? (Round your answer to
four decimal places.)
P =
(c) What is the approximate probability that x will differ
from μ by more than 0.8?...

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