The data in the table represents a company’s profit based on the number of items produced
1 answer:
Answer:
(A) y= -1.026x^2 + 1016.402x - 162075
Step-by-step explanation:
Here is the options to the question
Which equation best represents the data?
A) y= -1.026x^2 + 1016.402x - 162075
B) y= -1.036x^2 + 1024.771x - 163710
C) y= 298.214x - 66317.667
D) y= 196.2x – 18710
(A) y= -1.026x^2 + 1016.402x - 162075
The data above represents the company's profit based on number of items produced.
To get the equation which best represents the data, we have to substitute the value of x into the given equations
By substituting x=100 in first equation, we have:
y = -1.02x² + 1016.402x – 162075
y = -1.026(100)² + 1016.402(100) – 162075
y = -70500
y = -70500
Option A satisfies.
Using the second equation
When x = 100
y = -1.036x^2 + 1024.771x - 163710
y = -1.036(100)² + 1024.771(100) - 163710
y = -10360 + 102477.1 – 163710
y = -71592.9
Option B doesn’t satisfies
We can also replace the various values of x in the equations to check whether or not they satisfy.
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Answer:
(1)
(2)
The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025,0,1)", and we got , replacing into formula (2) we got:
So the answer for this case would be n=25 rounded up to the nearest integer
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean for the sample
population mean (variable of interest)
represent the population standard deviation
n represent the sample size (variable of interest)
The confidence interval for the mean is given by the following formula:
The margin of error is given by this formula:
(1)
And on this case we have that ME =0.02 and we are interested in order to find the value of n, if we solve n from equation (1) we got:
(2)
The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025,0,1)", and we got , replacing into formula (2) we got:
So the answer for this case would be n=25 rounded up to the nearest integer