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
Dmitry [639]
3 years ago
5

Laser scanning for fish volume estimation. engineers design tanks for rearing commercial fish to minimize both the use of natura

l resources (water) and the rearing volume necessary to ensure fish welfare.
One key to a well-designed tank is obtaining a reliable estimate of the volume (biomass) of fish reared in the tank.
The feasibility of a laser scanning technique for estimating fish biomass was investigated in the Journal of Aquacultural Engineering (Nov.2012). Fifty turbot fish were reared in a tank for experimental purposes.
A laser scan was executed in four randomly selected locations in the tank and the volume (in kilograms) of fish layer at each location was measured.
The four laser scans yielded a mean volume of 240 kg with a standard deviation of 15 kg. from this information, estimate the true mean volume of fish layer in the tank with 99% confidence. Interpret the result, practically.

What assumption about the data is necessary for the inference derived from the analysis to be valid?
Mathematics
1 answer:
AVprozaik [17]3 years ago
4 0

Answer:

The 99% confidence interval would be given by (196.2;283.8)

We are 99% condident that the true mean is between 196.2 and 283.8  

We need to assume that the data comes from a random sample and we need to assume that the distribution of the data is normal.  

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X=240 represent the sample mean for the sample  

\mu population mean (variable of interest)

s=15 represent the sample standard deviation

n=4 represent the sample size  

Part a

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=4-1=3

Since the Confidence is 0.99 or 99%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,3)".And we see that t_{\alpha/2}=5.84

Now we have everything in order to replace into formula (1):

240-5.84\frac{15}{\sqrt{4}}=196.2    

240+5.84\frac{15}{\sqrt{4}}=283.8

So on this case the 99% confidence interval would be given by (196.2;283.8)    

We are 99% condident that the true mean is between 196.2 and 283.8

What assumption about the data is necessary for the inference derived from the analysis to be valid?

We need to assume that the data comes from a random sample and we need to assume that the distribution of the data is normal.

You might be interested in
9. If 3/4 of a ton of sand covers 2/5 of a playground, how many tons of sand are required to cover the entire playground
Lynna [10]
1 7/8 tons of sand will be required to fill the playground

6 0
3 years ago
The sides of a rectangle have the ratio 7:2. its perimeter is 207cm.<br> Find the area
castortr0y [4]
X - unit of length
w,l - the sides of a rectangle

7 : 2 ⇒ 7x : 2x

Perimeter: P = 207cm
Perimeter: P = 2w + 2l

therefore: 2w + 2l = 207    |divide both sides by 2

w + l = 103.5 (cm)

w : l = 7 : 2 ⇒ w : l = 7x : 2x ⇒ w = 7x; l = 2x

subtitute

7x + 2x = 103.5
9x = 103.5    |divide both sides by 9
x = 11.5 (cm)

7x = 7 · 11.5cm = 80.5cm
2x = 2 · 11.5cm = 23cm

w = 80.5cm; l = 23cm

Area = wl

Area: A = 80.5cm · 23cm = 1851.5cm²
8 0
3 years ago
Find the area and circumference of the circle. Use 3.14 for A.
Kaylis [27]

Answer:

A = 63.59

C = 28.26

Step-by-step explanation:

r = 4.5

Area of a circle:

A = πr²

A = 3.14(4.5²)

A = 3.14(20.25)

A = 63.59

Circumference:

C = 2πr

C = 2(3.14)(4.5)

C = 28.26

8 0
3 years ago
Iodine-131, a radioactive substance that is effective in locating brain​ tumors, has a​ half-life of only 8 days. A hospital pur
Aloiza [94]

The mass of substance left after 7 days is 13.09 g

The mass of substance left, N is given by

N = N₀exp(-λt) where λ = decay constant and N₀ = initial mass of substance present = 24 g and t = time

Also, λ = 0.693/t' where t' = half-life of iodine = 8 days

So, λ = 0.693/t'

λ = 0.693/8

λ = 0.086625/day

Since the mass of substance left is N = N₀exp(-λt) and we require the mass of substance after t = 7 days,

N = N₀exp(-λt)

N = 24 gexp(-0.086625/day × 7 days)

N = 24 gexp(-0.606375)

N = 24 g × 0.5453

N = 13.09 g

So, the mass of substance left after 7 days is 13.09 g

Learn more about radioactive decay here:

brainly.com/question/23705307

7 0
3 years ago
What does positive correlation mean?
valina [46]

Answer:A positive correlation is a relationship between two variables such that their values increase or decrease together.

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Other questions:
  • Find the percent of increase to the nearest whole from 12 to 20
    11·1 answer
  • Write an equation of the line that passes through the point (2, 3) and is perpendicular to the line y = 1/2x - 1
    11·1 answer
  • What are the domain and range of this function?
    5·1 answer
  • Maureen makes $15 an hour at her job, plus an 18% bonus on her salary for that day if she sells a super item. Maureen worked 5 h
    6·1 answer
  • Miley has dax of playing cards write an equation for a function that shows how many c cards miley has altogether if each deck of
    13·1 answer
  • I’m not sure need help! ANSWER QUICKKK PLZZ
    7·1 answer
  • Michaels is using the rectangular board shown below to make a table top
    6·1 answer
  • A bookstore sells 3 books for $42. Which table represents the relationship between number of books and the total price?
    10·2 answers
  • Which of the following is required to construct the inscribed circle of a triangle?
    5·2 answers
  • Help please would be appreciated ​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!