Answer:
A sample of 997 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of 
, and a confidence level of 
, we have the following confidence interval of proportions.
In which
z is the z-score that has a p-value of 
.
The margin of error is of:
A previous study indicates that the proportion of left-handed golfers is 8%.
This means that 
98% confidence level
So 
, z is the value of Z that has a p-value of 
, so 
.
How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 2%?
This is n for which M = 0.02. So
Rounding up:
A sample of 997 is needed.
.98 since the hundredth place is higher than a five it is rounded up
Answer:
x=4
y=4√5
Step-by-step explanation:
Set up 3 right triangles and mark their respective angles. The largest will have sides (in typical a,b,c[hypotenuse] order) y, z, and 10. The middle 8, x, and y. The smallest x, 2, and z.
Then since they are all similar triangles, using the midde and smaller triangles, set up the proportionin which both A sides when divided are equal to the B sides.
So 8/x = x/2
Cross multiply and get 16=x^2.
The square root of 16 is 4, so x is 4.
Then using the larger and middle triangles, do the same for the A and C sides.
So y/8 = 10/y.
Cross multiply and get 80=y^2.
Find the square root of it, which since it doesn't have a perfect square, you use a calculator or the whatever theorem and get √4*4*5 or simply 4√5.
So x = 4 and y = 4√5
(-4,5) that is the distance between the two
