What theorem has been proven here?

First figure out what your full salary is, before the taxes. To do this, multiply 35 and 3 to get 105 hours total. Multiply this number and the salary, 105*8.25=866.25. Now you have to add the taxes up to figure out how much is deducted. 7.65+13+9=29.65% Multiply that number and the salary to find out how much is deducted. A shortcut for this is to multiply the 1 minus the tax and the salary, to find the total salary, but either way will give the same answer. The tax written in decimal form is 0.2965. (866.25)(1-0.2965)=609.4. if im wrong sorry hope this helped tho :p

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According to the Labor Department, the average duration of unemployment for adults ages 20 to 24 was 34.6 weeks during a recent

Misha Larkins [42]

Answer:

0.9173 = 91.73% probability that the average duration of unemployment was between 30 and 37 weeks.

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 $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 p-value, 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 $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .