Ava wants to know the distance JK across a pond. She locates points as shown. She says that the distance
1 answer:
Answer:
The answer is below
Step-by-step explanation:
Ava wants to know the distance JK across a pond. She locates points as shown. She says that the distance across the pond must be 160 ft by the SSS Triangle Congruence Theorem.
Solution:
Two triangles are said to be congruent if they their three sides are equal and their three angles are equal.
From the image attached we can say that triangle LMN and triangle JNK are congruent since they have they share the same angle (∠N) and both of their sides are equal. This is the side, angle, side (SAS) congruence theorem.
Hence since they are congruent, JK = 160 feet by the SAS triangle congruence theorem.
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Answer:
The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly 0.907 = 90.7%.
Step-by-step explanation:
To solve this question, we have to understand 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
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly
This probability is the pvalue of Z when X = 1600 + 300 = 1900 subtracted by the pvalue of Z when X = 1600 - 300 = 1300. So
X = 1900
By the Central Limit Theorem
has a pvalue of 0.9535.
X = 1300
has a pvalue of 0.0465.
0.9535 - 0.0465 = 0.907.
The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly 0.907 = 90.7%.
Answer:
A) 9 => 6 => 3 => 0 => -3 => -6
B) Using Formula
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