What is the simplest form of the expression?
1 answer:
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Answer:
a)
And we can conclude that we are 95% confident that the true mean of Co2 level is between 608.29 and 700.03 ppm
b)
Step-by-step explanation:
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 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,51)".And we see that
Replacing we got:
And we can conclude that we are 95% confident that the true mean of Co2 level is between 608.29 and 700.03 ppm
Part b
The margin of error is given by :
(a)
The desired margin of error is ME =50/2=25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
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 , and we use an estimator of the population variance the value of 175 replacing into formula (b) we got:
Answer:
The age of each person is:
- Jess is <u>21</u> years old.
- Mac is <u>66</u> years old.
Step-by-step explanation:
To solve this problem you must make two equations. First, we name Jess and Mac as variables:
j = Jess age.
m = Mac age.
Now we make the equations, the first equation has the information "Jess is 12 years less than half as old as Mac":
1.
The second equation has the information "The sum of their age is 87":
2.
Now, we replace the first equation in the second one:
And we operate:
We clear the variable m:
How we know Mac's age is 66 years old, we can identify Jess' age with the second equation:
We replace the value of m:
And clear the variable j:
In the end, Jess's age is 21 years old.