True or False? A circle could be circumscribed about the quadrilateral below.
1 answer:
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Using the <em>normal probability distribution and the central limit theorem</em>, it is found that the probabilities are given by:
a) 0.0119 = 1.19%.
b) 0.121 = 12.1%.
c) 0.9257 = 92.57%.
<h3>Normal Probability Distribution</h3>In a normal distribution with mean and standard deviation
, the z-score of a measure X is given by:
- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
In this problem:
- The mean is of
.
- The standard deviation is of
.
- A sample of 144 is taken, hence
.
Item a:
The probability is the <u>p-value of Z when X = 42600</u>, hence:
By the Central Limit Theorem:
has a p-value of 0.0119.
The probability is of 0.0119 = 1.19%.
Item b:
The probability is the <u>1 subtracted by the p-value of Z when X = 46240</u>, hence:
has a p-value of 0.879.
1 - 0.879 = 0.121.
The probability is of 0.121 = 12.1%.
Item c:
The probability is the <u>p-value of Z when X = 46980 subtracted by the p-value of Z when X = 43190</u>, hence:
X = 46980:
has a p-value of 0.9693.
X = 43190:
has a p-value of 0.0436.
0.9693 - 0.0436 = 0.9257.
The probability is of 0.9257 = 92.57%.
To learn more about the <em>normal probability distribution and the central limit theorem</em>, you can check brainly.com/question/24663213
Answer:
Option C is correct.
The exponential grows at twice the rate of the quadratic.
Step-by-step explanation:
Slope(rate) is given by:
As per the statement:
An exponential function and a quadratic function are graphed below.
In the given interval: [0, 1]
In Exponential function graph
Consider points (0, 1) and (1, 2)
then by definition of slope we have;
⇒Rate of exponential function is 2
In Quadratic function graph:
Consider points (0, 0) and (1, 1)
then by definition of slope we have;
⇒Rate of quadratic function is 1
⇒
Therefore, the exponential grows at twice the rate of the quadratic.
Answer:
a) 0.951
b) 2,800,000
c)
Step-by-step explanation:
Let R be a bounded and measurable region in the forest and denote with
|R| = area of R in acres
Let T(R) be a discrete random variable that measures the number of trees in the region R.
If the trees are distributed according to a two-dimensional Poisson process with the expected number of trees per acre equals to 40, then
(a) What is the probability that in a certain quarter-acre plot, there will be at most 15 trees?
In this case R is a region with an area of 1/4 acres,
We can compute this with a spreadsheet and we get
(b) If the forest covers 70,000 acres, what is the expected number of trees in the forest?
Given that the expected number of trees per acre equals 40, the expected number of trees in 70,000 acres equals
40*70,000 = 2,800,000 trees.
(c) Suppose you select a point in the forest and construct a circle of radius 0.1 mile. Let X = the number of trees within that circular region. What is the pmf of X?
Now R is a circle of radius 0.1 mile, so its area equals
Since 1 squared mile = 640 acres,
0.0314 squared miles = 0.0314*640 = 20.106 acres, so the pmf of R would be