MATHEMATICS COLLEGE

The United States Bureau of Labor Statistics (BLS) conducts the Quarterly Census of Employment and Wages (QCEW) and reports a variety of information on each county in America. In the third quarter of 2016, the QCEW reported the total taxable earnings, in millions, of all wage earners in all 3222 counties in America. Suppose that James is an economist who collects a simple random sample of the total taxable earnings of workers in 56 American counties during the third quarter of 2016. According to the QCEW, the true population mean and standard deviation of taxable earnings, in millions of dollars, by county are ?=28.29 and ?=33.493, respectively.
Let X be the total taxable earnings, in millions, of all wage earners in a county. The mean total taxable earnings of all wage earners in a county across all the counties in James' sample is x??.
Use the central limit theorem (CLT) to determine the probability P that the mean taxable wages in James' sample of 56 counties will be less than $33 million. Report your answer to four decimal places.
P(x??<33)=
Use the CLT again to determine the probability that the mean taxable wages in James' sample of 56 counties will be greater than $30 million. Report your answer to four decimal places.
P(x??>30)=

Answers

Answer 1

Answer:

Answer:

The probability is $P(\= X < 33) = 0.8531$

The probability is $P(\= X > 30) = 0.3520$

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 28.29$

The standard deviation is $\sigma = 33.493$

The sample size is $n = 56$

Generally the standard error for the sample mean $(\= x )$ is mathematically evaluated as

$\sigma _(\=x) = (\sigma)/(√(n) )$

substituting values

$\sigma _(\=x) = (33.493)/(√(56) )$

$\sigma _(\=x) = 4.48$

Apply central limit theorem[CLT] we have that

$P(\= X < 33) = [z < (33 - \mu )/(\sigma_(\= x)) ]$

substituting values

$P(\= X < 33) = [z < (33 - 28.29 )/(4.48) ]$

$P(\= X < 33) = [z < 1.05 ]$

From the z-table we have that

$P(\= X < 33) = 0.8531$

For the second question

Apply central limit theorem[CLT] we have that

$P(\= X > 30 ) = [z > (30 - \mu )/(\sigma_(\= x)) ]$

substituting values

$P(\= X < 33) = [z > (30 - 28.29 )/(4.48) ]$

From the z-table we have that

$P(\= X < 30) = 0.6480$

Thus

$P(\= X > 30) = 1- P(\= X < 30) = 1- 0.6480$

$P(\= X > 30) = 0.3520$

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The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second). (a) Find the probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.)

What is 35.5% of $210,000?

Answers

Answer:

$74,550

Step-by-step explanation:

On an exam, the mean score is 78 points, with a standard deviation of 6 points. Assuming normal distribution of the scores, approximately what percentage of students received more than 85?A.12% B.17% C.8% D.9% E.None of the above

Answers

Answer: A. 12%

Step-by-step explanation:-

Given : In an exam , Mean score : $\mu=78\text{ points}$

Standard deviation : $6\text{ points}$

Let X be a random variable that represents the scores of students.

We assume that the points are normally distributed.

Z-score : $z=(x-\mu)/(\sigma)$

For x = 85, we have

$z=(85-78)/(6)\approx1.17$

Then using standard normal distribution table, the probability that the students received more than 85 is given by :-

$P(x>85)=P(z>1.17)=1-P(z<1.17)\n\n=1-0.8789995=0.1210005\approx0.12=12\%$

Hence, the percentage of students received more than 85 =12%

A standard 52-card deck has four 13-card suits: diamonds, hearts, clubs, and spades. the diamonds and hearts are red, and the clubs and spades are black. each 13-card suit contains cards numbered from 2 to 10, a jack, a queen, a king, and an ace. an experiment consists of drawing 1 card from the standard deck. find the probability of drawing a black king of heartsblack king of hearts.

Answers

The probability of getting a black king of hearts is 1/52

From the question, we have:

The number of cards in a standard deck, n = 52

Black king of heart, r = 1

The probability of getting a black king of hearts is the quotient of the number of black king of heart and the total number of cards in the deck.

So, we have:

p = 1/52

Hence, the probability of getting a black king of hearts is 1/52

Answers

Answer:

D) 254.3

Step-by-step explanation:

The formula for the area of a circle is πr^2

so it would be, 3.14 x 9 x 9= 254.34

then just round your answer to the nearest tenth to get 254.3

Hope this helps! Let me know if you need help with anything else!

I need help with this one pleaseeeeeee (first will get brainliest)

Answers

Answer:

y = x + 15

Step-by-step explanation:

I tried all of them but that one works. U can try it on each number. Brainliest plz! Hope this helps!

Answer:

Y=2x is the answer

Step-by-step explanation:

Boatesville is a 65 3/5 -kilometer drive from stanton. A bus traveling from stanton to boatesville is 24 1/3 kilometers from boatesville. How far has the bus traveled