An aquarium tank in the shape of a rectangular prism is 60 cm long, 27 cm wide, and 24 cm high. the top of the tank is open, and
the glass used to make the tank is 1 cm thick. the volume for the aquarium is 33,350 cm3. what if, to provide greater strength, the glass bottom were increased to a thickness of 4 cm? how much less water would the tank hold?
1 answer:
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Answer:
n=350
Step-by-step explanation:
Notation and definitions
random sample taken (variable of interest)
estimated proportion (value assumed)
true population proportion
Confidence =0.95 or 95% (value assumed)
Me=0.05 (value assumed)
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".
The population proportion have the following distribution
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
And replacing into equation (b) the values from part a we got:
And rounded up we have that n=350