Which description best describes the solution to the following system of equations? y = –2x + 9 y = –x + 8 Lines y = –2x + 9 and
1 answer:
The equation represents a line, and so does the equation
This means that every point whose coordinates satisfy either of the two equations lies on that particular line
For example, point belongs to the first line, because
, and similarly the point
belongs to the second line, because
The solution of a system is a point whose coordinates satisfy both equations. This means, as we just saw, that this point lies on both lines.
So, the solution of a linear system is the point of intersection between the two lines.
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Answer:
64.76% probability that the mean diameter of the sample shafts would differ from the population mean by less than .2 inches
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 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
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
What is the probability that the mean diameter of the sample shafts would differ from the population mean by less than .2 inches?
This is the pvalue of Z when X = 200 + 0.2 = 200.2 subtracted by the pvalue of Z when X = 200 - 0.2 = 199.8. So
X = 200.2
By the Central Limit Theorem
has a pvalue of 0.8238
X = 199.8
has a pvalue of 0.1762
0.8238 - 0.1762 = 0.6476
64.76% probability that the mean diameter of the sample shafts would differ from the population mean by less than .2 inches