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:
There is no definite way to answer this question without further, more detailed information. I am truly sorry I am unable to answer this with the information provided.
Answer: There will be about 888,915 gallons of water left in the spherical tank.
First, we need to determine the volume of the tank. The volume formula for a sphere is (4/3)pi(r^3). All we have to do is input the 32 for pi and evaluate. You will have a volume of 137,189 cubic feet.
Now, multiply that by 7.5 and you will have 1,028,915 gallons of water in the tank.
Finally, just subtract the 140,000 gallons and we are at our answer.