Answer:
0.7486 = 74.86% observations would be less than 5.79
Step-by-step explanation:
I suppose there was a small typing mistake, so i am going to use the distribution as N (5.43,0.54)
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
The general format of the normal distribution is:
N(mean, standard deviation)
Which means that:
What proportion of observations would be less than 5.79?
This is the pvalue of Z when X = 5.79. So
has a pvalue of 0.7486
0.7486 = 74.86% observations would be less than 5.79
Little late, but your answer would be 133 pieces of candy corn.
Best of luck.
The <span>perimeter of a face of the new cube is 8 times larger than the previous cube.
</span>Let us say, the side of cube before increase is "a"
Then perimeter of the cube = 12a ,
because the cube has 12 sides.
And perimeter of a face of cube = 4a
Now, the side length is increased by factor of 3 i.e. new side is 3a
Thus, perimeter of new face of the cube = 4*3a = 12a
Therefore, the new perimeter is larger by = 12a - 4a = 8a
Answer:
The interval of convergence is:
Step-by-step explanation:
Given
The geometric series centered at c is of the form:
Where:
first term
common ratio
We have to write
In the following form:
So, we have:
Rewrite as:
Factorize
Open bracket
Rewrite as:
Collect like terms
Take LCM
So, we have:
By comparison with:
At c = 6, we have:
Take LCM
r = -\frac{1}{3}(x + \frac{11}{3}+6-6)
So, the power series becomes:
Substitute 1 for a
Substitute the expression for r
Expand
![\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}[(-\frac{1}{3})^n* (x - \frac{7}{3})^n]](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B3x%20%2B%202%7D%20%3D%20%20%5Csum%5Climits%5E%7B%5Cinfty%7D_%7Bn%3D0%7D%5B%28-%5Cfrac%7B1%7D%7B3%7D%29%5En%2A%20%28x%20-%20%5Cfrac%7B7%7D%7B3%7D%29%5En%5D)
Further expand:
The power series converges when:
Multiply both sides by 3
Expand the absolute inequality
Solve for x
Take LCM
The interval of convergence is:
The type of polynomial that would best model the data is a <em>cubic</em> polynomial. (Correct choice: D)
<h3>What kind of polynomial does fit best to a set of points?</h3>
In this question we must find a kind of polynomial whose form offers the <em>best</em> approximation to the <em>point</em> set, that is, the least polynomial whose mean square error is reasonable.
In a graphing tool we notice that the <em>least</em> polynomial must be a <em>cubic</em> polynomial, as there is no enough symmetry between (10, 9.37) and (14, 8.79), and the points (6, 3.88), (8, 6.48) and (10, 9.37) exhibits a <em>pseudo-linear</em> behavior.
The type of polynomial that would best model the data is a <em>cubic</em> polynomial. (Correct choice: D)
To learn more on cubic polynomials: brainly.com/question/21691794
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