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Zolol [24]
3 years ago
12

"Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested in the mean

amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was 7 hours with a sample standard deviation of 2.2 hours."
a. Define the random variables X and X- in words.
b. Which distribution should you use for this problem? Explain your choice.
c. Construct a 95% confidence interval for the population mean time wasted.
d. Explain in a complete sentence what the confidence interval means.
Mathematics
1 answer:
Digiron [165]3 years ago
7 0

Answer:

See Explanation Below

Step-by-step explanation:

Given

n = sample size = 81

u = mean wait time = 7 hours

σ = standard deviation = 2.2 hours

a

X is wait time per individual

X- is the mean of the sample means of size 81

b. Normal distribution

It's a distribution that occurs naturally in many situations; and it fits many natural phenomena. an example is given in the question above.

c.

x-bar = 7

To calculate the Margin of Error (ME)

For confidence Interval of 95%, the margin of error M.E = 1.96σ/√n

Where n = 81

M.E = 1.96 * 2.2 /√81

M.E = 0.48

So, the confidence Interval is given as follows

95% CI: 7-0.48 < u < 7+0.48

95% CI: 6.52 < u < 7.48

d. We are 95% confident that the population mean waiting time is

between 6.52 and 7.48 hours

You might be interested in
A large high school offers AP Statistics and AP Calculus Among the seniors in this school 65% take AP Statistics, 45% take AP Ca
Igoryamba

Answer:

0.8

Step-by-step explanation:

P(AP statistics) = 65%

P(AP Calculus) = 45%

P(AP statistics n AP Calculus) = 30%

Probability of AP statistics or AP Calculus but not both :

Probability of event A or B :

P(AUB) = p(A) + p(B) - p(AnB)

P(AP statistics U AP Calculus) = P(AP statistics) + P(AP Calculus) - P(AP statistics n AP Calculus)

= 0.65 + 0.45 - 0.30

= 0.8

= 80%

4 0
2 years ago
Diego and Lin are drinking milkshakes. Lin starts with 12 ounces and drinks 1/4 an ounce per second. Diego starts with 20 ounces
sammy [17]

Answer:

Lin = 48 seconds  

Diego = 30 seconds  

Step-by-step explanation:

Hi, to answer this question we have to divide the total ounces of drink by the amount that each one drank per second, for each case.

Mathematically speaking:

Lin = 12 ounces / (1/4) ounces/second = 12/ (1/4) = 48 seconds  

Diego = 20 ounces / (2/3) ounces/second = 20/ (2/3) = 30 seconds  

Feel free to ask for more if needed or if you did not understand something.

3 0
3 years ago
Please help me asap !!
Natasha2012 [34]

Answer:

3.5

Step-by-step explanation:

(42 - 14)/(12 - 4) = 28/8 = 7/2 = 3.5

5 0
2 years ago
Annual revenue for Corning Supplies grew by 5.5% in 2007; 1.1% in 2008; -3.5% in 2009; -1.1% in 2010; and 1.8% in 2011. What is
ANTONII [103]

Answer:

The mean growth annual rate over this period is 0.0036

Step-by-step explanation:

we know that

The mean growth annual rate is calculated as the sum of each year's growth rate divided by the number of years

\frac{5.5\%+1.1\%-3.5\%-1.1\%+1.8\%}{5}=0.36\%

Convert to decimal form

0.36\%=0.36/100=0.0036

therefore

The mean growth annual rate over this period is 0.0036

6 0
3 years ago
Solution for: <br> -x + 3y -2z = 19<br> 2x + y - z = 5<br> -3x - y + 2z = -7
STatiana [176]

Answer:

x = -1 , y = 4 , z = -3

Step-by-step explanation:

Solve the following system:

{-x + 3 y - 2 z = 19 | (equation 1)

2 x + y - z = 5 | (equation 2)

-3 x - y + 2 z = -7 | (equation 3)

Swap equation 1 with equation 3:

{-(3 x) - y + 2 z = -7 | (equation 1)

2 x + y - z = 5 | (equation 2)

-x + 3 y - 2 z = 19 | (equation 3)

Add 2/3 × (equation 1) to equation 2:

{-(3 x) - y + 2 z = -7 | (equation 1)

0 x+y/3 + z/3 = 1/3 | (equation 2)

-x + 3 y - 2 z = 19 | (equation 3)

Multiply equation 2 by 3:

{-(3 x) - y + 2 z = -7 | (equation 1)

0 x+y + z = 1 | (equation 2)

-x + 3 y - 2 z = 19 | (equation 3)

Subtract 1/3 × (equation 1) from equation 3:

{-(3 x) - y + 2 z = -7 | (equation 1)

0 x+y + z = 1 | (equation 2)

0 x+(10 y)/3 - (8 z)/3 = 64/3 | (equation 3)

Multiply equation 3 by 3/2:

{-(3 x) - y + 2 z = -7 | (equation 1)

0 x+y + z = 1 | (equation 2)

0 x+5 y - 4 z = 32 | (equation 3)

Swap equation 2 with equation 3:

{-(3 x) - y + 2 z = -7 | (equation 1)

0 x+5 y - 4 z = 32 | (equation 2)

0 x+y + z = 1 | (equation 3)

Subtract 1/5 × (equation 2) from equation 3:

{-(3 x) - y + 2 z = -7 | (equation 1)

0 x+5 y - 4 z = 32 | (equation 2)

0 x+0 y+(9 z)/5 = (-27)/5 | (equation 3)

Multiply equation 3 by 5/9:

{-(3 x) - y + 2 z = -7 | (equation 1)

0 x+5 y - 4 z = 32 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Add 4 × (equation 3) to equation 2:

{-(3 x) - y + 2 z = -7 | (equation 1)

0 x+5 y+0 z = 20 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Divide equation 2 by 5:

{-(3 x) - y + 2 z = -7 | (equation 1)

0 x+y+0 z = 4 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Add equation 2 to equation 1:

{-(3 x) + 0 y+2 z = -3 | (equation 1)

0 x+y+0 z = 4 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Subtract 2 × (equation 3) from equation 1:

{-(3 x)+0 y+0 z = 3 | (equation 1)

0 x+y+0 z = 4 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Divide equation 1 by -3:

{x+0 y+0 z = -1 | (equation 1)

0 x+y+0 z = 4 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Collect results:

Answer:  {x = -1 , y = 4 , z = -3

6 0
3 years ago
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