Sec square 75 degree + cot square 15 degree
2 answers:
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Answer:
0.1790
0.0738 , 0.5800, 0.7040
354
Step-by-step explanation:
a. Given:
n = 162
x = 29
c = 95%
The point estimate of the population proportion is the sample proportion. The sample proportion is the number of successes divided by the sample size:
p = x/n
= 29/162
= 0.1790
b. Given:
n=162
x = 110
c = 95%
The point estimate of the population proportion is the sample proportion. The sample proportion is the number of successes divided by the sample size:
p = x/n
=110/162
=0.6790
For confidence level 1 – = 0.95, determine z_
/2 = z_0.025 using table 1 (look up 0.025 in the table, the z-score is then the found z-score with opposite sign):
z_/2 = 1.96
The margin of error is then:
E = z_/2*√p(1-p)/n =1.96* √0.6790(1-0.6790)/162 =0.0738
The boundaries of the confidence interval are then:
p-z_/2*√p(1-p)/n = 0.6790-1.645√ 0.6790(1- 0.6790)/162 = 0.5800
p+z_/2*√p(1-p)/n = 0.6790+1.645√ 0.6790(1- 0.6790)/162 = 0.7040
c. Given:
n = 162
x = 110
c = 95%
The point estimate of the population proportion is the sample proportion. The sample proportion is the number of successes divided by the sample size:
p =x/n
=0.6790
Formula sample size:
p known: n = [z_/2 ]^2*pq/E^2
= [z_/2 ]^2*p(1-p)/E^2
n = [z_/2 ]^2*0.25/E^2
For confidence level 1 –= 0.95, determine z_
/2 = z_o.025 using table 1 (look up 0.025 in the table, the z-score is then the found z-score with opposite sign):
z_/2 = 1.96
p is known, then the sample size is (round up!):
n =[z_/2 ]^2*p(1-p)/E^2
= 354
We can eliminate choice C because our parabola is not upside down. The way I determined which one it was was by picking a point on the graph and testing the x value of the point in the equation. If the y value on the graph was the same as the y value on my calculator, then I chose the right one. Let me give you an example of what doesn't work first. Let's pick (3, 2) from the graph. Let's test that point in choice D. Filling in x = 3, y should = 2 if that's the right equation. 
. Our y coordinate is not 7/2, it's 2. Let's try A: 
. Again, our y value is 2, not -2. Let's try B: 
. See how that works? Your choice is B.