Find the perimeter of the rectrangle with vertices at R(-2, 3), S(4, 3), T(4, -1) and U(-2, -1).
1 answer:
I attached a photo where I graphed these vertices in order to count the length and width. After counting the number of units between R & U I got a width of 4. And then I counted the units between S & T to get a width of 6. Using the formula to calculate the perimeter of a rectangle, P = 2(l+w). The perimeter is 20.
First I added the length plus the width, 4 + 6 and got 10. Then I did 10 x 2 which is how I got a perimeter of 20.
First I added the length plus the width, 4 + 6 and got 10. Then I did 10 x 2 which is how I got a perimeter of 20.
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Answer:
0.4010 = 40.10% probability that the sample mean would differ from the population mean by more than 0.8 millimeters
Step-by-step explanation:
To solve this question, we need to understan the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
Either the sample mean differs by 0.8 mm or less from the population mean, or it differs by more. The sum of these probabilities is decimal 1.
Probability it differs by less than 0.8mm
pvalue of Z when X = 139 + 0.8 = 139.8mm subtracted by the pvalue of Z when X = 139 - 0.8 = 138.2 mm
X = 139.8
By the Central Limit Theorem
has a pvalue of 0.7995
X = 138.2
has a pvalue of 0.2005
0.7995 - 0.2005 = 0.5990
What is the probability that the sample mean would differ from the population mean by more than 0.8 millimeters?
p + 0.5990 = 0.4010
0.4010 = 40.10% probability that the sample mean would differ from the population mean by more than 0.8 millimeters