Mr. McLean manages playgrounds for the 8 elementary schools in the Franklin School District. This year, he wants to put new sand
2 answers:
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Answer:
Step-by-step explanation:
Using Pythagoras theorem , since it is a right angled triangle ,
side 1 = 10cm
side 2 = x cm
side 3 = x cm
Pythagoras theorem states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides. That is
100 =
divide through by 2 , we have
50 =
find the square root of both sides
Answer:
And rounded we got 1681
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
Solution to the problem
The population proportion have the following distribution
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 estimates proportion is 0.5 since we don't have other info provided to assume a different value. And replacing into equation (b) the values from part a we got:
And rounded we got 1681