answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Leya [2.2K]
2 years ago
9

The United States Bureau of Labor Statistics (BLS) conducts the Quarterly Census of Employment and Wages (QCEW) and reports a va

riety 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)=
Mathematics
1 answer:
Firlakuza [10]2 years ago
3 0

Answer:

1

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

2

  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} =  \frac{\sigma}{\sqrt{n} }

substituting values  

       \sigma _{\=x} =  \frac{33.493}{\sqrt{56} }

      \sigma _{\=x} = 4.48

Apply central limit theorem[CLT] we have  that

        P(\= X < 33) =  [z <  \frac{33 -  \mu }{\sigma_{\= x}} ]

substituting values

       P(\= X < 33) =  [z <  \frac{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 >  \frac{30 -  \mu }{\sigma_{\= x}} ]

substituting values

   P(\= X < 33) =  [z >  \frac{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

You might be interested in
What two integers does the square root of 429 lie?
Lubov Fominskaja [6]
The answer should be Two and Three ... 
7 0
2 years ago
Alex has 3 baseballs. He brings 2 baseballs to school. What fraction of his baseballs does Alex bring to school?
ivann1987 [24]
2/3 2/3 shows 2 out of 3, in this case meaning 2 out of 3 baseballs
7 0
1 year ago
Read 2 more answers
A student claims that the expression “9 times the sum of a number and 13” is translated to the algebraic expression 9n + 13. Is
Alex73 [517]
9*13+n 
I think that is correct, try and split up the question. 
9* 
A sum of a number AND 13
So that means that 9 is multiplying by the SUM (adding) of 13 and a number (n)
8 0
2 years ago
Read 2 more answers
Which statement describes a process to solve sqrt b+20 - sqrt b=5?
babunello [35]

Answer:

Step-by-step explanation:

The equation is:

√b+20 - √b = 5

The first step is we will add √b to both sides:

√b+20 -√b +√b = 5 +√b

√b+20 = 5+√b

Now take square at both sides:

(√b+20)^2 = (5+√b)^2

b+20 = 25+10√b+b

Now combine the like terms:

b+20-25-b=10√b

-5 = 10√b

Divide both the terms by 10

-5/10 = 10√b/10

-1/2=√b

Take square at both sides:

(-1/2)^2 = (√b)^2

1/4 = b

So in this type of question we add radical terms to both sides and square both sides twice....

7 0
1 year ago
Helen drove from the restaurant to the toy store, which
Morgarella [4.7K]

Answer:

4,3

Step-by-step explanation:

4,3

6 0
2 years ago
Other questions:
  • A train is traveling up slight grade with an angle of inclination of only 2 degrees. After traveling 1 mile, what is the vertica
    13·1 answer
  • Round 4.265 to the nearest hundredth
    8·1 answer
  • Suppose you earned 7t -1 dollars on monday and 8t + 5 on tuesday. what are your total earnings? simplify your answer
    8·1 answer
  • Ms. Valenzuela had her students design a snake house for the zoo. In the de3sign shown, the anaconda has 538 more square feet th
    8·1 answer
  • a rectangle rug has a perimeter of 146 ft the width of the rug is 5 feet more than three times the length find the length and th
    14·2 answers
  • An equiangular triangle has one side of length six inches. What is the height of the triangle, drawn from that side, to the near
    10·1 answer
  • Which expression is equivalent to logw((x^2-6)^4/(cube root x^2+8))
    14·2 answers
  • A conductor is mapping a trip and records the distance the train travels over certain time intervals.
    7·1 answer
  • Which is equivalent to-2(4-3x)+ (5x-2)
    11·1 answer
  • A cylinder is filled up with water to 3 4 its total capacity. The solid sphere is dropped completely into the cylinder. How high
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!