Clint found the area of the parallelogram shown. Which statement explains the error Clint made?
2 answers:
Answer:
D
Step-by-step explanation:
The area of a parallelogram is denoted by: , where b is the base and h is the height that is perpendicular to the base. Depending on what kind of parallelogram it is (square, rectangle, rhombus, regular parallelogram), that height <em>could</em> be the side length, but usually it is not; it is only the side length in special cases, like a square.
Here, we are given that the base is 11 and that the height is 4. Since the problem gives us two different values for the height versus the side length, we know that for this parallelogram, the height is not the same as the side length. Thus, we must use 4 for the height and 11 for the base in the area formula.
Therefore, the only answer that correctly points out this mistake is D.
Hope this helps!
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Step-by-step explanation:
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Answer:
96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
A reminder is that the standard deviation is the square root of the variance.
Normal probability distribution
When the distribution is normal, we use 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 normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
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For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
Probability that the mean of the sample would differ from the population mean by less than 126 miles
This is the pvalue of Z when X = 3639 + 126 = 3765 subtracted by the pvalue of Z when X = 3639 - 126 = 3513. So
X = 3765
By the Central Limit Theorem
has a pvalue of 0.983
X = 3513
has a pvalue of 0.017
0.983 - 0.017 = 0.966
96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles