Answer:
Anna's walk as a vector representation is and refer attachment.
Step-by-step explanation:
Let the origin be the point 1 from where Ann start walking.
Ann walks 80 meters on a straight line 33° north of the east starting at point 1 as shown in figure below,
Resolving into the vectors, the vertical component will be 80Sin33° and Horizontal component will be 80Cos33° as shown in figure (2)
Ann walk as a vector representation is
Thus, Anna's walk as a vector representation is
Answer:
1) n=48
2) n=298
3) n=426
Step-by-step explanation:
Previous concepts
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".
represent the real population proportion of interest
represent the estimated proportion for the sample
n is the sample size required (variable of interest)
represent the critical value for the margin of error
The population proportion have the following distribution
Part 1
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 90% 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)
We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:
And rounded up we have that n=48
Part 2
The margin of error on this case changes to 0.04 so if we use the same formula but changing the value for ME we got:
And rounded up we have that n=298
Part 3
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)
We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:
And rounded up we have that n=426