18 divided by tan 30
2 answers:
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Answer:
a)
b) The 98% confidence interval would be given by (8.44;9.84)
For this case we can conclude that we have 98% of confidence that the true mean for the oxygen content is between 8.44 and 9.84 mg/L
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=44 represent the sample size
Part a
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Since the Confidence is 0.98 or 98%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that
Now we have everything in order to replace into formula (1):
Part b
The 98% confidence interval would be given by (8.44;9.84)
For this case we can conclude that we have 98% of confidence that the true mean for the oxygen content is between 8.44 and 9.84 mg/L
The equations are
,
The graphs of the solutions (x, y) of these equations are 2 parabolas, since the right hand side expressions are polynomials of degree 2.
The solution/s of the system are the x-coordinates of the point/s of intersection of the parabolas.
The solutions of the first equation form a parabola looking downwards (since the coefficient of x^2 is -), and the second, a parabola opening upwards (since the coefficient of x^2 is +).
We can draw both parabolas, but to find the solution we still need to solve the system algebraically.
The algebraic solution of the system is:
, so
the solutions are x=-1 and x=1.
The graph of the system is drawn using desmos.com
If we are allowed to use a graphic calculator, we can draw both graphs and point at the solution.
The graphs of the solutions (x, y) of these equations are 2 parabolas, since the right hand side expressions are polynomials of degree 2.
The solution/s of the system are the x-coordinates of the point/s of intersection of the parabolas.
The solutions of the first equation form a parabola looking downwards (since the coefficient of x^2 is -), and the second, a parabola opening upwards (since the coefficient of x^2 is +).
We can draw both parabolas, but to find the solution we still need to solve the system algebraically.
The algebraic solution of the system is:
the solutions are x=-1 and x=1.
The graph of the system is drawn using desmos.com
If we are allowed to use a graphic calculator, we can draw both graphs and point at the solution.