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Murrr4er [49]
3 years ago
15

Adam Zetts is an aerospace engineer. He earns $78,000 a year

Mathematics
1 answer:
Firlakuza [10]3 years ago
6 0

Answer:

Social Security: $201.50, Medicare: $47.13

Step-by-step explanation:

divide 78,000 by 24(semimonthly) - $78000/24 = $3250(gross semimonthly basis)

multiply 3250 by .062(social security) - 3250 x .062 = $201.50

multiply 3250 by 0.0145(medicare) - 3250 x 0.0145 = $47.13

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The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 48,564 miles, with a standard
DerKrebs [107]

Answer:

0.0091 = 0.91% probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct

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 can be solved using 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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 48564, \sigma = 3293, n = 281, s = \frac{3293}{\sqrt{281}} = 196.44

What is the probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct?

This is the pvalue of Z when X = 48101. So

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{48101 - 48564}{196.44}

Z = -2.36

Z = -2.36 has a pvalue of 0.0091

0.0091 = 0.91% probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct

6 0
2 years ago
The area of a square bedroom is 144 square feet. what is the length of one wall?
Rufina [12.5K]
The answer is:  "12 feet" .
________________________________
Note:  In a square, the length of EACH of the four sides of the square is the same.

Area = Length * width. 

For a square, length = width.

So for a square, Area = length * width = (length of a side)² = s² ,

Given:  A = s² = 144 ft² ;

Solve for the positive value of "s" .
________________________________
  →  s² = 144 ft² ;  Take the "square root" of each side ;

  → √(s²) = √(144 ft²) ;

  →   s = 12 ft.
_______________________________
The answer is:  12 ft.
_______________________________
6 0
3 years ago
Three out of every ten dentists recommend a certain brand of fluoride toothpaste. Which assignment of random digits would be use
Len [333]

Answer:

b

Step-by-step explanation:

only b has 10 didgets. it could be a since the didgets aren't very random, but then again, i think it's b

5 0
3 years ago
Harvey has a 3qt container and a 5qt container. How can he measure 4 qt of water
Snowcat [4.5K]

harvey can mesure 3 qrt in the 3 qrt container and 1 qrt in the 5qrt container

7 0
3 years ago
Line b passes through points (5, 5) and (10, 8). Line c passes through points (4, 8) and (1, 13). Are line b and line c parallel
lora16 [44]

Answer:

Step-by-step explanation:

In going from (5, 5) to (10, 8), x (the run) increases by 5 and y (the rise) increases by 3.  Thus, the slope of the line connecting the first two points is m = 3/5.

In going from (1, 13) to (4, 8), x (the run) increases by 3 and y (the rise) decreases by 5.  Thus, the slope of the line connecting the first two points is m = -5/3

Because these results are negative reciprocals of one another, the two lines are PERPENDICULAR to one another.

3 0
3 years ago
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