1answer.
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
ZanzabumX [31]
2 years ago
6

The 2008 Workplace Productivity Survey, commissioned by LexisNexis and prepared by World One Research, included the question, "H

ow many hours do you work at your job on a typical workday." Let x = the number of hours a legal professional works on a typical workday. Suppose that x is normally distributed with a known standard deviation of 12.6.
A sample of 250 legal professionals was surveyed, and the sample's mean response was 9 hours. Use the sample information to estimate μ, the mean number of hours a legal professional works on a typical workday. Develop a 95% confidence interval estimate of the mean number of hours a legal professional works on a typical workday.
Mathematics
1 answer:
LenaWriter [7]2 years ago
5 0

Answer:

A 95% confidence interval estimate of the mean number of hours a legal professional works on a typical workday is [7.44 hours, 10.56 hours].

Step-by-step explanation:

We are given that x is normally distributed with a known standard deviation of 12.6.

A sample of 250 legal professionals was surveyed, and the sample's mean response was 9 hours.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                               P.Q.  =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample average mean response = 9 hours

            \sigma  = population standard deviation = 12.6

            n = sample of legal professionals = 250

            \mu = mean number of hours a legal professional works

<em>Here for constructing a 95% confidence interval we have used One-sample z-test statistics as we know about population standard deviation.</em>

<u>So, 95% confidence interval for the population mean, </u>\mu<u> is ;</u>

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                   of significance are -1.96 & 1.96}  

P(-1.96 < \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < 1.96) = 0.95

P( -1.96 \times {\frac{\sigma}{\sqrt{n} } } < {\bar X-\mu} < -1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

P( \bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } } < \mu < \bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

<u>95% confidence interval for</u> \mu = [ \bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } } , \bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } } ]

                                       = [ 9-1.96 \times {\frac{12.6}{\sqrt{250} } } , 9+1.96 \times {\frac{12.6}{\sqrt{250} } } ]

                                       = [7.44 hours, 10.56 hours]

Therefore, a 95% confidence interval estimate of the mean number of hours a legal professional works on a typical workday is [7.44 hours, 10.56 hours].

You might be interested in
Carly is pouring sand into a rectangular container with dimensions of 4 1/2 inches by 3 1/2 inches by 2 inches. What is the maxi
Pachacha [2.7K]
The answer is 31.5 in.^3 because
4.5 • 3.5 • 2 = 31.5in.^3
8 0
3 years ago
Read 2 more answers
Help me !!!!!!!!!!!!!???
Nesterboy [21]

Answer:

what are you supposed to be doing

7 0
2 years ago
Read 2 more answers
An airplane cuts through the morning sky. For every 1,000 feet that it climbs, the outside temperature drops 20 degrees Fahrenhe
andreyandreev [35.5K]

The air plane is rising so the change in elevation is +1000 feet. The temp dropped and is -20 degrees fahrenheit.

1 degree per 50 ft

For every 1,000 feet that it climbs, the outside temperature drops 20 ... What is the rate of temperature change in degrees Fahrenheit per foot.

8 0
2 years ago
The depth of a swimming pool is 8.5 meters. What half of the depth is in millimeters?
timofeeve [1]
4250 millimeters.
Half of 8.5m is 4.25m.
4.25 m to mm is 4250.
4 0
3 years ago
Read 2 more answers
Michaela signed a 5-year contract for her new job and her starting salary is $67K ($67,000) per year. If she gets a good review
Elena L [17]

Answer:

79,180

Step-by-step explanation:

you start off with 67k and multiply it by 1.03 for every outcome untill after 5th year

5 0
2 years ago
Other questions:
  • Choose the slope-intercept form of y + 3 = 4(x - 5).
    14·2 answers
  • The total cost of all of the ingredients for her cakes is $62<br> She will sell each cake for $10
    11·1 answer
  • 720 m/day = m/min <br> Show work.
    11·1 answer
  • The expression 3 1/2x + 18 represents the perimeter of the rectangle shown. Write an expression that represents the length of th
    11·1 answer
  • What is 347,168 round to then thoudands
    6·2 answers
  • At Grab &amp; Go Grocery, you can buy 4 yogurt cups for $5. If the unit price stays the same, how much would it cost to buy 10 y
    5·1 answer
  • NO LINKS OR FILES. Explain how to evaluate 5p + (-6) when p = -4. Please give an explanation.
    10·2 answers
  • The College Board originally scaled SAT scores so that the scores for each section were approximately normally distributed with
    10·1 answer
  • What is the length of the radius of the circle given the equation ( x + 5)² + (y - 6)² = 49?
    9·1 answer
  • Ivana has two identical dice and on the faces of each are the numbers −3, −2, −1, 0, 1, 2.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!