The following data sets can be modeled linearly. Data Set M: {(14,95),(9,85),(4,65),(6,80),(3,73),(12,107),(7,64),(12,86),(10,96
),(9,64),(1,44)} Data Set N: {(13,109),(9,85),(4,65),(6,80),(3,63),(12,107),(7,76),(11,100),(10,96),(8,85),(1,44)} Use technology to find the correlation coefficient of each data set.
Part A: Which data set has a better linear model?
Part B: How do you know this?
B: Data set M has a correlation coefficient that is closer to 1.
B: Data set M has a higher correlation coefficient.
A: Data set M has a better linear model.
B: Data set N has a correlation coefficient that is closer to 1.
B: Data set N has a lower correlation coefficient.
A: Data set N has a better linear model.
Part A: Which data set has a better linear model?
Part B: How do you know this?
B: Data set M has a correlation coefficient that is closer to 1.
B: Data set M has a higher correlation coefficient.
A: Data set M has a better linear model.
B: Data set N has a correlation coefficient that is closer to 1.
B: Data set N has a lower correlation coefficient.
A: Data set N has a better linear model.
1 answer:
Answer:
The data set <em>N</em> has a better linear model.
Step-by-step explanation:
The data for the two data sets is:
Data Set M: {(14,95), (9,85), (4,65), (6,80), (3,73), (12,107), (7,64), (12,86), (10,96), (9,64), (1,44)}
Data Set N: {(13,109), (9,85), (4,65), (6,80), (3,63), (12,107), (7,76), (11,100), (10,96), (8,85), (1,44)}
The Correlation coefficient can be computed in Excel using the function:
CORREL(array1, array2)
Consider the table attached below for the correlation for data M and N.
Correlation coefficient for data M = 0.81
Correlation coefficient for data N = 0.99
Closer the correlation value is to 1 or -1, the better is the linear model.
This is because the correlation value of 1 or -1 are considered as perfect correlation.
The correlation coefficient for data N is 0.99 which is approximately equal to 1.
Thus, the data set <em>N</em> has a better linear model.
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Answer:
<h2>a. It should look for 3 linear factors.</h2><h2>b. There are 3 dimensions.</h2><h2>c. x = 1.7</h2><h2>d. Maximum value is 12.597</h2>Step-by-step explanation:
a.
=
=
=
Hence the factorized form of the volume of the poly is
3 linear factors should needed to be look for.
b.
The 3 dimensions are (x + 4), x, (x + 3).
c.
Let, f(x) =
Now, =
Let =
and
=
=
The value will be maximum, if f1(x) = 0 and f2(x) < 0.
\\
\\
x = 1.69 ≅ 1.7 or x = -2.36 ≅ -2.4
Now f2(1.7) < 0.
At x = 1.7, the volume will be maximum.
d.
The maximum value is f(1.7) = 12.597(approximately)
Answer:
The warranty period should be of 30 months.
Step-by-step explanation:
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.
Optimal-Eats blender has a mean time before failure of 37 months with a standard deviation of 5 months.
This means that
What should be the warranty period, in months, so that the manufacturer will not have more than 7% of the blenders returned?
The warranty period should be the 7th percentile, which is X when Z has a p-value if 0.07, so X when Z = -1.475.
Rounding to the nearest whole number, 30.
The warranty period should be of 30 months.