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The midpoint is (5, ¹/₂).
<h3>Further explanation</h3>The midpoint is the coordinates of a point right in the middle of a line segment or two endpoints.
The Midpoint Formula
So, abscissa and ordinate of the midpoint are the averages of both endpoints. i.e., (x₁, y₁) and (x₂, y₂).
Given (x₁, y₁) = (5, 4) and (x₂, y₂) = (5, -3).
Let's calculate the midpoint.
We get the midpoint between the two endpoints, that is, (5, ¹ / ₂).
<h3>Learn more</h3>- Finding a line that is not parallel to either the x-axis or the y-axis and passes through a point brainly.com/question/4691222
- Finding the equation, in slope-intercept form, of the line that is parallel to the given line and passes through a point brainly.com/question/1473992
- A line segment is a piece of a line with two endpoints brainly.com/question/909890
Keywords: the midpoint, the line segment, endpoints, in the middle, between, average, abscissa and ordinate, the coordinates
Answer:
39.36% probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than 0.17.
Step-by-step explanation:
For each couple, there are only two possible outcomes. Either they are mixed racially or ethnically, or they are not. This means that the binomial probability distribution is used to solve this problem.
However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be 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.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
So
When n = 100, what is the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than 0.17?
This is 1 subtracted by the pvalue of Z when . So:
has a pvalue of 0.6064.
So there is a 1-0.6064 = 0.3936 = 39.36% probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than 0.17.