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
Annette [7]
3 years ago
10

Color-blindness is any abnormality of the color vision system that causes a person to see colors differently than most people or

to have difficulty distinguishing among certain colors (www.visionrx.xom).Color-blindness is gender-based, with the majority of sufferers being males.Roughly 8% of white males have some form of color-blindness, while the incidence among white females is only 1%.A random sample of 20 white males and 40 white females was chosen.Let X be the number of males (out of the 20) who are color-blind.Let Y be the number of females (out of the 40) who are color-blind.Let Z be the total number of color-blind 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.e. The remaining questions refer to the following information:
Mathematics
1 answer:
Veronika [31]3 years ago
3 0

Answer:

Correct option is (d): Neither X nor Y can be well-approximated by a normal random variable.

Step-by-step explanation:

The sample size of males having color-blindness is, n (X) = 20.

The sample size of females having color-blindness is, n (Y) = 40.

The proportion of males that suffer from color-blindness is, P (X) = 0.08.

The proportion of females that suffer from color-blindness is, P (Y) = 0.01.

Now both the random variables <em>X</em> and <em>Y</em> follows a Binomial distribution,

X\sim Bin(20, 0.08)\\Y\sim Bin(40, 0.01)

A normal distribution is used to approximate the binomial distribution if the sample is large, i.e <em>n</em> ≥ 30 and the probability of success is very close to 0.50.

Also if <em>np</em> ≥ 10 and <em>n</em> (1 - <em>p</em>) ≥ 10, the binomial distribution can be approximated by the normal distribution.

<u>For the sample of men (X):</u>

np=20\times0.08=1.610

In this case neither <em>n</em> > 30 nor <em>p</em> is close to 0.50.

And <em>np</em> < 10.

Thus, the random variable <em>X</em> cannot be approximated by the normal distribution.

<u>For the sample of men (Y):</u>

np=40\times0.01=0.410

In this case <em>n</em> > 30 but <em>p</em> is not close to 0.50.

And <em>np</em> < 10.

Thus, the random variable <em>Y</em> cannot be approximated by the normal distribution.

Thus, both the random variables cannot be approximated by the normal distribution.

The correct option is (d).

You might be interested in
Answer the questions below in your own handwriting. Typed responses will not be accepted. When you are finished, scan/save this
Dmitry [639]

Answer:

Lawns ---Earnings

1 ----------------- 10

2 ----------------- 20

3 ----------------- 30

5 ----------------- 50

Step-by-step explanation:

Given

Earnings = $10 per lawn

Required

Complete the table

Let y be the earnings for x number of lawns

Since he earns $10 per x lawns, then the expression is:

y = 10x

To complete the table, we have the following:

When x = 1

y = 10 * 1 = 10

When x = 2

y = 10 * 2 = 20

When x = 3

y = 10 * 3 = 30

When x = 5

y = 10 * 5 = 50

So, the complete table is:

Lawns ---Earnings

1 ----------------- 10

2 ----------------- 20

3 ----------------- 30

5 ----------------- 50

5 0
3 years ago
Find the solution to each number sentence below:
Feliz [49]

Answer:

1. 5

2. -1

3.-41

4. 55

5.-155

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
In triangle MPQ points N and R are located on sides MP and QP with NR drawn. which set of measurements below would justify that
NNADVOKAT [17]
The answer is number 1. Because 12/10 =20/18 is a true statement. None of the others are true
6 0
2 years ago
What is the slope of the line? y-3=5
ivolga24 [154]
Undefined is the answer for me. Lol
5 0
3 years ago
Read 2 more answers
Convert 6 miles to meters​
Iteru [2.4K]

Answer:

9656.06 meters

Step-by-step explanation:

5 0
2 years ago
Other questions:
  • the height of the gem stone is 2.668 centimeters. the volume of the gem stone is 7.4793cubic centimeters. what is the side lengh
    7·1 answer
  • How to find an unknown measure of the rectangle if the perimeter is 54 how they got 54
    13·2 answers
  • What is this he gcf for 32 and 52
    7·1 answer
  • fairveiw has 330 seventh grade students, and is ratio of boys to girls is 6:5. salem has 360 seventh grade students, and its rat
    14·1 answer
  • Simplify the following expression:<br><br> 3(2x-6) + 4(-3x + 8)
    10·1 answer
  • If a donut costs 50 cents and a cookie costs 35 cents, write an
    12·1 answer
  • 5800 dollars is placed in an account with an annual interest rate of 9%. To the nearest tenth of a year, how long will it take f
    13·1 answer
  • Im so confused so PLS HHELP !!!!!! ;-;
    13·1 answer
  • This is my last question ​
    6·2 answers
  • What is the slope-intercept equation<br> for the following line?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!