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
hoa [83]
3 years ago
15

Functionally important traits in animals tend to vary little from one individual to the next within populations, possibly becaus

e individuals who deviate too much from the mean have lower fitness. If this is the case, does variance in a trait rise after it becomes less functionally important? Billet et al. (2012) investigated this question with the semicircular canals (SC) of the three-toed sloth (Bradypus variegatus). The authors proposed that since sloths don't move their heads much, the functional importance of SC is reduced, and may vary more than it does in more active animals. They obtained the following measurements of the ratio of the length to width of the anterior SC in 6 sloths. Assume this represents a random sample. In other, more active animals, the standard deviation of this ratio is 0.09.

Mathematics
1 answer:
Jet001 [13]3 years ago
8 0

Answer:

The 95% confidence interval for the standard deviation is (0.14, 0.54).

Step-by-step explanation:

The complete data and question is:

Sloth CW Ratios ; {1.5 , 1.09 , 0.98 , 1.42 , 1.49 , 1.25}

The 95% confidence interval for the standard deviation of this data is  < σ <   (two decimals - include the leading zero) .

Solution:

Compute the sample standard deviation as follows:

\bar x=\frac{1}{n}\sum x=\frac{1}{6}\times 7.73=1.2883\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{6-1}\times 0.2387}=0.2185

The (1 - <em>α</em>)% confidence interval for the variance is:

CI=\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2}}

Confidence level = 95%

⇒ α = 0.05

The degrees of freedom is,

df = n - 1 = 6 - 1 = 5

Compute the critical values of Chi-square:

\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.025,5}=12.833\\\\\chi^{2}_{1-\alpha/2, (n-1)}=\chi^{2}_{0.975,5}=0.831

*Use a Chi-square table.

Compute the 95% confidence interval for the variance as follows:

CI=\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2}}

     =\frac{5\times (0.2185)^{2}}{12.833}

Thus, the 95% confidence interval for the standard deviation is (0.14, 0.54).

You might be interested in
530 : 34 =?<br> Write your answer as a whole number and remainder.
Scorpion4ik [409]
168 and 7 as remainder
3 0
3 years ago
Read 2 more answers
A culture started with 5000 bacteria after 5 hours it grew to 6500 bacteria predict how many bacteria will be present after 16 h
postnew [5]

Answer:

After 16 hours bacterial count will be 11600.

Step-by-step explanation:

Bacterial growth is always an exponential growth in a given culture.So the formula for the growth will be

Final counts of bacteria = Initial counts × (rate of growth)^{time}

Given from first part Initial counts = 5000

Final counts= 6500 and time of growth = 5 hours

Then we will get the value of rate of growth of bacteria from the bacteria

⇒ 6500 = 5000×(rate)^{5}

(rate)^{5}= \frac{6500}{5000} = 1.3

Rate = \sqrt[5]{1.3} = 1.05

Now again to get the value of bacteria after 16 hours

Final Count = 5000×(1.05)^{16}

                   = 5000×2.32

                   = 11600


7 0
3 years ago
If a coin is tossed 5 times, and then a standard six-sided die is rolled 4 times, and finally a group of three cards are drawn f
Step2247 [10]

Answer:  5,499,187,200

<u>Step-by-step explanation:</u>

A coin is tossed 5 times.  

There are two options (heads or tails) so the possible outcomes are: 2⁵

A six-sided die is rolled 4 times.

There are six options so the possible outcomes are: 6⁴

A group of 3 cards are drawn (without replacement).

The first outcome has 52 options, the second has 51 options, and the third has 50 options: 52 x 51 x 50

Now if we want the coin AND the die AND the cards, we have to multiply all of their possible outcomes:

     2⁵ x   6⁴  x  52 x 51 x 50

=   32 x 1296 x 132,600

=  5,499,187,200

3 0
3 years ago
If there is an 80% chance of rain and a 10% chance of wind and rain, what is the probability that it is windy, given that it is
dalvyx [7]
13% (apex) is the correct answer 
4 0
3 years ago
A rectangle is four times as long as it is wide. If its length were diminished by 6 meters and its width were increased by 6 met
valkas [14]

Answer:

Length equals 16 and Width equals 4

Step-by-step explanation:

First let us create an equation. We can use L and W for length and width.

If the length is 4 times the width, then we end up with: L = 4W

It then says, " If its length were diminished by 6 meters and its width were increased by 6 meters, it would be a square."

Since a square has an equal length and width then we end up with:

L - 6 = W + 6

Knowing this we can just substitute the first equation into the second one leaving us with: 4W - 6 = W + 6

We then remove a W from both sides so that the right side is left with a 6, and add 6 to both sides to remove the -6 from the left one.

This leaves us with 3W = 12

W = 4, and if we put that into our first equation, L = 4W, then Length equals 16, and Width equals 4. We can check this by putting it into the 2nd equation. 16 - 6 = 4 + 6.

7 0
1 year ago
Other questions:
  • Solve the given quadratic equation. x^2=121
    14·2 answers
  • 3x - 4y =7 solve for y
    9·2 answers
  • A bow is made from 2 2/3 yards of ribbon. Which expression gives the number of bows that can be made from 22 5/8 yards?
    7·2 answers
  • PLEASEE help me!!
    10·1 answer
  • The conjugate is used in _____ of complex numbers.
    15·2 answers
  • Find the value of x, will give brainlist
    10·1 answer
  • The account title are:
    13·1 answer
  • Which of the following shows that the product of two irrational numbers can be rational?
    5·1 answer
  • What is The equation of a circle with radius, r= 4, and the center at (0, 0)?
    11·1 answer
  • On a scale drawing, 9 inches<br> represents 11 miles. How many<br> inches represent 55 miles?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!