Yesterday's afternoon temperature was 21*F. It plunged overnight to 3*F. How many degrees did the temperature drop? I think the
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Answer:
So without prior estimation for the population proportion, using a confidence level of 95% if we want a margin of error about 2% we need al least a sample size of 2401.
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".
The population proportion have the following distribution
Solution to the problem
The margin of error for the proportion interval is given by this formula:
(a)
If solve n from equation (a) we got:
(b)
The margin of error desired for this case is equivalent to 2% points
For this case we need to assume a confidence level, let's assume 95%. And since we don't have prior estimation for the population proportion of interest the best value to do an approximation is
In order to find the critical value we need to take in count that we are finding the margin of error 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:
Now we have all the values needed and if we replace into equation (b) we got:
So without prior estimation for the population proportion, using a confidence level of 95% if we want a margin of error about 2% we need al least a sample size of 2401.
Answer:
Step-by-step explanation:
Triangle MAB is similar to triangle MNP
Since the triangles are similar, the corresponding ratios are in the same proportion.
Therefore we can write the relation;
This implies that;
We multiply both sides by 72.6 to get
Hence the value of is 50.6 cm