You are constructing triangle ABC given the line segments AB and AC and ∠A. The first thing you do is copy segment AC. Next, you
copy angle A using A on the segment AC as the vertex. What is the next step? A) Copy ∠A again. B) Connect point B to point C. C) Copy AB. D) Construct a line parallel to AC
1 answer:
Answer:
C) Copy AB
Step-by-step explanation:
The general idea is that you copy one segment, then the angle (so you know which direction the other segment goes), then the second segment. Finally, you connect the ends of the segments to complete the triangle.
The given description says you've done the first two parts of this, so you must mark off the length of segment AB in the direction you just constructed. That is, you must ...
Copy AB.
_____
In the attached figure, the construction did segment AB first, and is about to do segment AC next. The idea is the same. Swap points B and C in your mind to match the description in the problem statement.
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Answer:
a) 33% probability that a single student randomly chosen from all those taking the test scores 21 or higher.
b) 0.39% probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher
Step-by-step explanation:
To solve this question, we need 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
, 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:
a) What is the probability that a single student randomly chosen from all those taking the test scores 21 or higher?
This is 1 subtracted by the pvalue of Z when X = 21. So
has a pvalue of 0.67
1 - 0.67 = 0.33
33% probability that a single student randomly chosen from all those taking the test scores 21 or higher.
b) The average score of the 76 students at Northside High who took the test was x =20.4. What is the probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher?
Now we have
This probability is 1 subtracted by the pvalue of Z when X = 20.4. So
By the Central Limit Theorem
has a pvalue of 0.9961
1 - 0.9961 = 0.0039
0.39% probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher