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
natulia [17]
3 years ago
13

Left-handedness occurs in about 12% of all Americans. Males are slightly more likely than females to be left-handed, with 13% of

males and 11% of females being left-handed. Suppose a random sample of 80 females and 100 males is chosen.
-Let X be the number of males (out of the 100) who are left-handed.

-Let Y be the number of females (out of the 80) who are left-handed.

-Let Z be the total number of left-handed individuals in the sample (males and females together).

Which of the following is true regarding the random variables X and Y?

a)Both X and Y can be well approximated by normal random variables.
b)Only X can be well approximated by a normal random variable.
c)Only Y can be well approximated by a normal random variable.
d)Neither X nor Y can be well approximated by a normal random variable.
Mathematics
1 answer:
FinnZ [79.3K]3 years ago
5 0

Answer:

a)Both X and Y can be well approximated by normal random variables.

Step-by-step explanation:

For each individual, there are only two possible outcomes. Either they are right-handed, or they are left-handed. This means that we can solve this problem using concepts of the binomial probability distribution.

Binomial probability:

Probability of exactly x sucesses on n repeated trials, with probability p.

The binomial probability can be well approximated by normal random variables, using the expected value E(X) = np and the standard deviation \sigma = \sqrt{np(1-p)}

Let X be the number of males (out of the 100) who are left-handed.

n = 100 and p = 0.13. Can be well approximated.

Let Y be the number of females (out of the 80) who are left-handed.

n = 80 and p = 0.11. Can be well approximated.

The correct answer is

a)Both X and Y can be well approximated by normal random variables.

You might be interested in
Which is equivalent to √60n^11/256n^4 after it has been simplified completely? Assume n =0
motikmotik

Answer:

\large\boxed{\dfrac{n^3}{8}\sqrt{15n}}

Step-by-step explanation:

\sqrt{\dfrac{60n^{11}}{256n^4}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\ \text{and}\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\=\sqrt{\dfrac{60}{256}n^{11-4}}=\dfrac{\sqrt{60n^7}}{\sqrt{256}}=\dfrac{\sqrt{4n^{6+1}\cdot15}}{16}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=\dfrac{\sqrt{4n^6\cdot15n}}{16}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\dfrac{\sqrt{4n^{3\cdot2}}\cdot\sqrt{15n}}{16}\qquad\text{use}\ (a^n)^m=a^{nm}

=\dfrac{\sqrt{4(n^3)^2}\cdot\sqrt{15n}}{16}=\dfrac{\sqrt{4}\cdot\sqrt{(n^3)^2}\cdot\sqrt{15n}}{16}=\dfrac{2\!\!\!\!\diagup^1\sqrt{15n}}{16\!\!\!\!\!\diagup_8}=\dfrac{n^3\sqrt{15n}}{8}

5 0
3 years ago
When you are making a fraction with a whole number in it how do you set it up after dividing it
Aloiza [94]

Answer:

Does this help?

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
jessica is ordering 3 bags of cat food from Canada. Each bag has a mass of 5 kg. To determine the shipping cots, Jessica needs t
Kazeer [188]
The total weight in pounds is 33.0693 lbs
8 0
3 years ago
Read 2 more answers
Perimeter Formula, P=2L+2W (there is a picture with the remaining information)
Dvinal [7]
The answer is 76 other wise it will be -9
4 0
3 years ago
Delete the ribbon is 3/4 meter Sunday needs pieces measuring 1/3 meter for in our project what is the greatest number of pieces
Bogdan [553]

Answer:the greatest number of pieces that can be cut is 2

Step-by-step explanation:

The total length of ribbon available is 3/4 meter. Sunday needs pieces measuring 1/3 meter for their project. This means that each length needed would be exactly 1/3 meter.

The number of pieces measuring 1/3 meter that can be cut from the ribbon would be

(3/4)/(1/3) = 3/4×3/1 = 9/4 = 2.25

Since the length needed is exactly 1/3 meter, the greatest number of pieces that can be cut will be 2

6 0
3 years ago
Other questions:
  • Brandy’s grandfather has a very old pet tortoise He told Brandy that the tortoise was 56 years old when she was born 11 years ag
    8·1 answer
  • What is the center and radius of the circle with equation (x - 2)^2 + (y - 5)^2 = 100?
    11·2 answers
  • Melvin borrowed $1,200 for furniture. His monthly payments were $60 for 24 months. Find the total amount repaid.
    14·2 answers
  • Which is greater 2 2/3, 2.45, 2 2/5
    13·2 answers
  • Which of the following is not a type of propaganda?
    5·1 answer
  • PLEASE NEED HELP ASAP WILL MARK BRAINLIEST Question 2 of 10
    11·1 answer
  • Someone help please<br><br> Find the sine of
    6·1 answer
  • HELP THIS IS DUE SOON,, THE QUESTION IS ON THE PHOTO
    11·2 answers
  • Hi again,
    13·2 answers
  • Which inequality represents the sentence below? The difference of a number and one and four tenths is more than nine and seventy
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!