Solve my question please, I’ll mark u as brainlest if you solved my question!!!
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Answer:
IS a parallelogram
Step-by-step explanation:
The slope formula for the slope of the line between points (x1, y1) and (x2, y2) is ...
m = (y2 -y1)/(x2 -x1)
The distance formula for the length of that same line is ...
d = √((x2 -x1)^2 +(y2 -y1)^2)
Here, you're asked to use each of these formulas 4 times, once for each side of the quadrilateral. I find it convenient to let a calculator or spreadsheet do the repetitive calculations. The result is attached.
The attachment shows that opposites sides have the same length and slope, so are parallel. The quadrilateral is a parallelogram. (The two points used in each calculation are the ones on the result line and the line immediately below. That is why point B is copied to the end of the list.)
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<em>Additional comments</em>
There are much simpler ways to prove the figure is a parallelogram. My favorite is to add the coordinates of the end points of the diagonals:
B +D = (-2+6, -9-3) = (4, -12)
C +E = (0+4, -5-7) = (4, -12)
These values being the same demonstrates the midpoints of the diagonals are coincident. That will only be the case if the quadrilateral is a parallelogram.
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If you must use slope and distance formulas, showing either pair of opposite sides is parallel and have the same length is sufficient to guarantee that the other two sides are also parallel and have the same length. That is, the calculations required in this problem only need to be applied to one pair of opposite sides. (Using a spreadsheet, it's not a lot of extra work to do the calculations for both pairs of opposite sides.)
Answer:
a) 0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.
b) 0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.
c) 0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The mean of a population is 74 and the standard deviation is 15.
This means that
Question a:
Sample of 36 means that
This probability is 1 subtracted by the pvalue of Z when X = 78. So
By the Central Limit Theorem
has a pvalue of 0.9452
1 - 0.9452 = 0.0548
0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.
Question b:
Sample of 150 means that
This probability is the pvalue of Z when X = 77 subtracted by the pvalue of Z when X = 71. So
X = 77
has a pvalue of 0.9929
X = 71
has a pvalue of 0.0071
0.9929 - 0.0071 = 0.9858
0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.
c. A random sample of size 219 yielding a sample mean of less than 74.2
Sample size of 219 means that
This probability is the pvalue of Z when X = 74.2. So
has a pvalue of 0.5793
0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2