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2 years ago

Solve the problem using 6.2%, up to $128,400 for Social Security tax and using 1.45%, no wage limit, for Medicare tax.

Mathematics

1 answer:

N76 [4]2 years ago

7 0

Based on the Social security tax and the Medicare tax, the amounts for the payroll manager are:

Social security - $145.70
Medicare - $216.78

<h3>What are the Social security and Medicare taxes?</h3>

The Social Security tax is charged on up to $128,400 and the Payroll manager had a salary of $141,000 so far but only $14,950 this month so the social security tax will be calculated:

= 6.2% x (128,400 - (141,000 - 14,950))

= $145.70

The Medicare tax has no limit:

= 14,950 x 1.45%

= $145.70

Monthly Social security:

= 7,960.80 / 12

= $216.78

Find out more on Medicare tax at brainly.com/question/23706698

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Let X represent the full height of a certain species of tree. Assume that X has a normal distribution with a mean of 137.1 ft an

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0.0668 = 6.68% probability that the height of a randomly selected tree is as tall as mine or shorter.

0.0228 = 2.28% probability that the full height of a randomly selected tree is at least as tall as hers.

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When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 137.1, \sigma = 3.2$

A tree of this type grows in my backyard, and it stands 132.3 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter.

This is the pvalue of Z when X = 132.3. So

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

$Z = \frac{132.3 - 137.1}{3.2}$

$Z = -1.5$

$Z = -1.5$ has a pvalue of 0.0668

0.0668 = 6.68% probability that the height of a randomly selected tree is as tall as mine or shorter.

My neighbor also has a tree of this type growing in her backyard, but hers stands 143.5 feet tall. Find the probability that the full height of a randomly selected tree is at least as tall as hers.

This is 1 subtracted by the pvalue of Z when X = 143.5. So

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

$Z = \frac{143.5 - 137.1}{3.2}$