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keidyhernandezm
08.03.2021 •
Mathematics
Jean works for the government and was conducting a survey to determine the income levels of a number of different neighborhoods in a metropolitan area. Based on national data, Jean knows that the mean income level in the country is $40,000, with a standard deviation of $2,000. Jean selected three neighborhoods and determined the average income level. What is the probability that the average income level in the neighborhoods was less than $38,000
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Ответ:
0.0418 = 4.18% probability that the average income level in the neighborhoods was less than $38,000.
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 normal distributions 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.
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.
Jean knows that the mean income level in the country is $40,000, with a standard deviation of $2,000.
This means that![\mu = 40000, \sigma = 2000](/tpl/images/1178/7093/80e32.png)
Jean selected three neighborhoods and determined the average income level.
This means that![n = 3, s = \frac{2000}{\sqrt{3}} = 1154.7](/tpl/images/1178/7093/01ccc.png)
What is the probability that the average income level in the neighborhoods was less than $38,000
This is the pvalue of Z when X = 38000. So
By the Central Limit Theorem
0.0418 = 4.18% probability that the average income level in the neighborhoods was less than $38,000.
Ответ:
(A) AA similarity
Step-by-step explanation:
Given: AB is parallel to DE.
To prove: △ACB is similar to △DCE.
Proof: It is given that AB is parallel to DE, thus because the lines are parallel and segment CB crosses both lines, we can consider segment CB a transversal of the parallel lines.
Now, from △ACB and △DCE, we have
∠CED≅∠CBA (corresponding angles of transversal CB and are therefore congruent)
and ∠C ≅ ∠C (Reflexive property)
Thus, by AA similarity postulate,
△ACB is similar to △DCE
Hence proved.
Thus, option A is correct.