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
Tcecarenko [31]
2 years ago
15

A certain type of bird lives in two regions of a state. The distribution of weight for birds of this type in the northern region

is approximately normal with mean 10 ounces and standard deviation 3 ounces. The distribution of weight for birds of this type in the southern region is approximately normal with mean 16 ounces and standard deviation 2.5 ounces.(a) Calculate the z-scores for a weight of 13 ounces for a bird living in the northern region and for a weight of 13 ounces for a bird living in the southern region.(b) Is it more likely that a bird of this type with a weight greater than 13 ounces lives in the northern region or the southern region? Justify your answer.
Mathematics
1 answer:
harkovskaia [24]2 years ago
7 0

Answer:

a) Z for northern region = 1 , Z for southern region = -1.2

b) Southern region

Step-by-step explanation:

a) Z = (x – mean)/standard deviation

Le x be weight for birds

For the northern region  

Z = (13 – 10)/3

Z = 1

For the southern region

Z = (13 – 16)/2.5

Z = -1.2

b) to find in what region is more likely to find a bird with 13 ounces, we calculate the probability for each z value

For the northern region  

P (x>13) = P(z > 1)

Then we use the z table to find the area under the curve.

P (x>13) = 0.1587

For the southern region

P (x>13) = P(z > 1.2)

Then we use the z table to find the area under the curve.

P (x>13) = 0.8849

Is it more likely that a bird with a weight greater than 13 ounces lives in the southern region

You might be interested in
Your friend Alex is planning a fundraising game night to raise money for a local children's hospital. She invites a few of your
katrin [286]

Step-by-step explanation:

(a) You win $5 if you roll a six, $1 if you roll an odd number, and $0 if you roll a 2 or a 4, and you pay $1.50 for every roll.  The expected value is the sum of each outcome multiplied by its probability.

E = (5.00)(1/6) + (1.00)(3/6) + (0)(2/6) + (-1.50)(1)

E = -0.167

You are expected to lose on average about $0.17 per roll, which means Alex has the advantage.

(b) The probability of rolling a 2 or 4 on a fair die is 2/6 or 1/3.  The probability of this happening five times is:

P = (1/3)⁵

P = 1/243

P ≈ 0.41%

There is approximately a 0.4% probability that a fair die will roll a 2 or 4 five times.

(c) The confidence interval for a proportion is:

CI = p ± ME

ME = CV × SE

The margin of error is the critical value times the standard error.

The critical value for 95% confidence is z = 1.960.

The standard error for a proportion is:

SE = √(pq/n)

Given p = 1/6, q = 5/6, and n = 100:

SE = √((1/6) (5/6) / 100)

SE = 0.037

So the confidence interval is:

CI = 1/6 ± (1.960) (0.037)

CI = 0.167 ± 0.073

0.094 < p < 0.240

Since the observed proportion of 0.08 is outside of this interval, we can conclude with 95% confidence that the die is not fair.

(d) Under the current game rules and die probabilities, the expected value is:

E = (5.00)(0.08) + (1.00)(0.33) + (0)(0.59) + (-1.50)(1)

E = -0.77

To make the game fairer, but to still give Alex the advantage so she can make money for her fundraiser, we need to change the rules of the game so that the expected value is less negative.

One simple way to do this is to pay players $2.00 if they roll a 2.

Now the expected value is:

E = (5.00)(0.08) + (1.00)(0.33) + (2.00)(0.29) + (0)(0.30) + (-1.50)(1)

E = -0.19

Now instead of expecting to lose on average $0.77 per roll, players can expect to lose on average $0.19 per roll.  This means they have a better chance of winning money, but Alex still has the advantage.

8 0
3 years ago
Sjsjjsnsnsjdjdjkdkdkdkdkddkdidkdkdkkdkxkxkxkxkkxmxnxmxmxkmxkxkxkkxkx
almond37 [142]
Sknsmakskdnndjaixjnejwjc :)
5 0
3 years ago
Read 2 more answers
Sam gets paid a set rate in his allowance for making his bed every morning. His rate is $0.50 earned for every morning that he m
AlekseyPX

Answer:

bottom graph of left picture

Step-by-step explanation:

For each day he makes his bed, he earns $0.50

In 1 day he earns $0.50

In 2 days he earns $1.00

In 3 days, he earns $1.50

...

In 8 days, he earns $4.00

Look in the 4 graphs.

Which graph has the following points, (1, 0.5), (2, 1), 3, 1.5), ... , (8, 4)?

It is the second graph (bottom graph of left picture.)

4 0
2 years ago
Triangle ABC is similar to triangle WYZ.
Inga [223]

9514 1404 393

Answer:

  False

Step-by-step explanation:

Corresponding angles in similar triangles are congruent. The similarity statement tells you angle B corresponds to angle Y, so those angles are congruent. The sines of congruent angles are identical.

  sin(B) > sin(Y) . . . . FALSE

  sin(B) = sin(Y) . . . . true

7 0
2 years ago
Which of the following is a secant?
taurus [48]

A secant is simply a line that intersects the circle at exactly two points.

Therefore, line GH is a secant of circle

B since it intersects the circle ast 2 points.

4 0
3 years ago
Other questions:
  • Which equation can be rewritten as x + 4 = x^2? Assume x &gt; 0
    7·2 answers
  • Complete the equation of the line through (−10,3) (−8,−8). Use exact numbers. y=
    8·1 answer
  • Please help!!!! Brainliest worth 15 points
    11·2 answers
  • THIS IS HARD FOR M I NEED HELP!!!!!
    8·2 answers
  • Help w algebra problem!!!
    12·1 answer
  • Please help, question is above in picture
    9·1 answer
  • A full one- gallon container can be
    5·1 answer
  • Keiko sold 3 less than three-fourths of his sister's sales. Which expression represents what Keiko sold?
    12·2 answers
  • Please show step by step need it now
    10·1 answer
  • If the length of a rectangle is 6 more than twice the width and the total perimeter is 84cm, what is the rectangle's length?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!