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
algol [13]
3 years ago
11

Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, 33% of all homeowners are ins

ured against earthquake damage. Four homeowners are to be selected at random. Let X denote the number among the four who have earthquake insurance. A) Find the probability distribution of X.B) What is the most likely value for X?
C) What is the probability that at least two of the four selected have earthquake insurance?
Mathematics
1 answer:
Lina20 [59]3 years ago
3 0

Answer:

(a) The probability mass function of <em>X</em> is:

P(X=x)={4\choose x}\ (0.33)^{x}\ (1-0.33)^{4-x};\ x=0,1,2,3...

(b) The most likely value for <em>X</em> is 1.32.

(c) The probability that at least two of the four selected have earthquake insurance is 0.4015.

Step-by-step explanation:

The random variable <em>X</em> is defined as the number among the four homeowners  who have earthquake insurance.

The probability that a homeowner has earthquake insurance is, <em>p</em> = 0.33.

The random sample of homeowners selected is, <em>n</em> = 4.

The event of a homeowner having an earthquake insurance is independent of the other three homeowners.

(a)

All the statements above clearly indicate that the random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 4 and <em>p</em> = 0.33.

The probability mass function of <em>X</em> is:

P(X=x)={4\choose x}\ (0.33)^{x}\ (1-0.33)^{4-x};\ x=0,1,2,3...

(b)

The most likely value of a random variable is the expected value.

The expected value of a Binomial random variable is:

E(X)=np

Compute the expected value of <em>X</em> as follows:

E(X)=np

         =4\times 0.33\\=1.32

Thus, the most likely value for <em>X</em> is 1.32.

(c)

Compute the probability that at least two of the four selected have earthquake insurance as follows:

P (X ≥ 2) = 1 - P (X < 2)

              = 1 - P (X = 0) - P (X = 1)

              =1-{4\choose 0}\ (0.33)^{0}\ (1-0.33)^{4-0}-{4\choose 1}\ (0.33)^{1}\ (1-0.33)^{4-1}\\\\=1-0.20151121-0.39700716\\\\=0.40148163\\\\\approx 0.4015

Thus, the probability that at least two of the four selected have earthquake insurance is 0.4015.

You might be interested in
A. (x, y) → (x, y + 4)
Harrizon [31]
X444444xxx-xxxx444468
3 0
2 years ago
1) Apples cost $16 for an 8 pound bag at the local price
bija089 [108]

Answer:

4 pounds with a membership

29 pounds without

i just added both because i didnt know if you meant 58 extra dollars after bbuying membership or not

Step-by-step explanation:

58 -50(membership fee)=8

16 divide by 8=2

16$=8 pounds

8$=4 pounds

---------------------------------------

without membership you could buy 29 pounds of apples

58 divide by 16=3.625

3.625 x 8=29

3 0
1 year ago
Point A bisects LS BC. If LS BA=6x-3 and LS AC= 3x+7. Solve for X. PLS ANSWER QUICKLY!!!
denis23 [38]

Based on the bisection of line BC by point A, the value of x is 10/3

<h3>How to determine the value of x?</h3>

The given parameters are:

  • Point A bisects BC
  • BA = 6x - 3
  • AC= 3x + 7

Because the point A bisects BC, then

BA = AC

Substitute the known values in the above equation

So, we have

6x - 3 = 3x + 7

Collect the like terms

6x - 3x = 3 + 7

Evaluate the like terms

3x = 10

Divide both sides of the equation by 3

x = 10/3

Hence, based on the bisection of line BC by point A, the value of x is 10/3

Read more about bisectors at:

brainly.com/question/6725549

#SPJ1

8 0
1 year ago
What is the range of this data set? {14, 25, 61, 18, 30, 32, 28, 45, 21} 47 28 7 I don't know.
kati45 [8]

The range of the dataset = 47

What is the range of a dataset?

The range of a set of data is the difference between the greatest number and least number

The given data set is:

{14, 25, 61, 18, 30, 32, 28, 45, 21}

The greatest number = 61

The least number = 14

The range of the dataset = Greatest Number - Least Number

The range of the dataset = 61  -  14

The range of the dataset = 47

Learn more on range of a distribution here: brainly.com/question/4679134

3 0
2 years ago
Read 2 more answers
ANSWER ASAP! I'LL MARK BRAINLIEST :)
AleksAgata [21]
Hope this helps!
X>-2
7 0
3 years ago
Other questions:
  • 4. Write a word problem for 3/4 X 1/2! Please help me!!
    7·1 answer
  • In the figure, lines a, b, and c are parallel and m∠4=68° . Drag and drop the correct angle measure for each angle. m∠1 = m∠2 =
    5·2 answers
  • Write two decimals that are equivalent to 3.7
    9·2 answers
  • How to find the square root
    11·1 answer
  • Do any three points not on the same line always, sometimes, or never determine a plane? Explain
    7·1 answer
  • Draw coins to show 39cents. Describe how to count to find the total value of this group of coins.
    13·2 answers
  • of the 75 boys in the 7th grade class, 25 participate in at least one sport . of the 120 girls in 7th grade class 30
    14·1 answer
  • Can the quotient of two irrational numbers ever be a rational number?
    9·2 answers
  • Divide 15 to the 7th power by 6 then add 66 brainly
    9·1 answer
  • Simplify the expression.<br> - (m<br> m + 3n - 13)
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!