Answer:
95% Confidence interval for the mean

Step-by-step explanation:
We have to calculate a 95% confidence interval for the mean of a finite population.
The error is multiplied by the following finite population correction factor:

The standard deviation can be estimated as

The 95% confidence interval has a z value of 1.96, so it becomes:

Problem 1
Answer: Closer to 1
Explanation:
There are 20 gumballs total. Half of this is 20/2 = 10 gumballs. If there's more than 10 of one color, then the probability of getting that color is closer to 1, than it is to 0. Here we have 12 pink which is greater than 10, so that's why the answer is closer to 1.
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Problem 2
Answer: Closer to 0
Explanation:
The amount of green (3) is less than 10, so that's why the probability is closer to 0 than it is to 1. We can see that 3/20 = 0.15 is less than 0.50
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Problem 3
Answer: Closer to 0
Explanation:
We have a similar situation compared to problem 2. This time we have 5/20 = 0.25 which is less than 0.50
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Problem 4
Answer: 48% chance; fairly likely
Explanation:
We have 12 green out of 25 total, so the probability of choosing green is 12/25 = 0.48 = 48%. While this probability is not over 50%, I still say it's fairly likely considering the other colors lead to smaller probabilities. For instance, purple has a chance of 6/25 = 0.24 = 24% and orange has a probability of 2/25 = 0.04 = 4%, both of which are smaller than 48%
Answer: 
Step-by-step explanation:
Sine uses the ratio,
so we can plug in the information we know. since there is no current value for the opposite side of angle A, we can just use a variable to replace it.

You can't reduce this any further because there is an unknown variable.
as a fraction of 180, m < 1 = 1/ (1 + 3 + 2) * 180 = 1/6 * 180 = 30 degrees
m < 2 = 3*30 = 90 degrees
and m < 3 = 30*2 = 60 degrees
Answer: 2p+1.50=11.50
p = 5.00
<u>Step-by-step explanation:</u>
<em>Note: the tip is calculated on top of the total so this figure is a redherring</em>
<u>2 pancakes</u> <em>plus</em> <u>1 fruit cup</u> <em>equals</em> <u>total bill</u>
2p + 1.50 = 11.50
2p + 1.50 = 11.50
<u> - 1.50 </u> <u> - 1.50 </u>
2p = 10.00
<u>÷2 </u> <u> ÷2 </u>
p = 5.00