In a county containing a large number of rural homes, 60% of the homes are insured against fire. Four rural homeowners are chosen at random from this county, and x are found to be insured against fire. Find the probability distribution for x.

Answers

Answer 1

Answer:

[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}[/tex]

Step-by-step explanation:

Given

[tex]p = 60\%[/tex]

[tex]n = 4[/tex]

Required

The distribution of x

The above is an illustration of binomial theorem where:

[tex]P(x) = ^nC_x * p^x *(1 - p)^{n-x}[/tex]

This gives:

[tex]P(x) = ^4C_x * (60\%)^x *(1 - 60\%)^{n-x}[/tex]

Express percentage as decimal

[tex]P(x) = ^4C_x * (0.60)^x *(1 - 0.60)^{n-x}[/tex]

[tex]P(x) = ^4C_x * (0.60)^x *(0.40)^{4-x}[/tex]

When x = 0, we have:

[tex]P(x=0) = ^4C_0 * (0.60)^0 *(0.40)^{4-0}[/tex]

[tex]P(x=0) = 1 * 1 *(0.40)^4[/tex]

[tex]P(x=0) = 0.0256[/tex]

When x = 1

[tex]P(x=1) = ^4C_1 * (0.60)^1 *(0.40)^{4-1}[/tex]

[tex]P(x=1) = 4 * (0.60) *(0.40)^3[/tex]

[tex]P(x=1) = 0.1536[/tex]

When x = 2

[tex]P(x=2) = ^4C_2 * (0.60)^2 *(0.40)^{4-2}[/tex]

[tex]P(x=2) = 6 * (0.60)^2 *(0.40)^2[/tex]

[tex]P(x=2) = 0.3456[/tex]

When x = 3

[tex]P(x=3) = ^4C_3 * (0.60)^3 *(0.40)^{4-3}[/tex]

[tex]P(x=3) = 4 * (0.60)^3 *(0.40)[/tex]

[tex]P(x=3) = 0.3456[/tex]

When x = 4

[tex]P(x=4) = ^4C_4 * (0.60)^4 *(0.40)^{4-4}[/tex]

[tex]P(x=4) = 1 * (0.60)^4 *(0.40)^0[/tex]

[tex]P(x=4) = 0.1296[/tex]

So, the probability distribution is:

[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}[/tex]


Related Questions

WHERE ARE THE EXPERTS AND ACE!!!!!!! I NEED HELP PLS SHARE YO SMARTNESS!!!!! WILL GIVE BRAINLIEST AND RATE AND VOTE!!! EASY IM JUST NOT SMART

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Answer:

a7 = 55 + (7-1) 10

Step-by-step explanation:

See,

It's given that it will take 7 hours for Jiya to move.

$55 are charged for 1 (first) hour. Now, 6 hours are left (unpaid). $10 per every hour after that.

Among the total 7 hours, the payment for first hour is done ($55) so we are left with the other 6 hours multiplied by 10.

Therefore, the correct option is:

a7 = 55 + (7-1) 10


HELP PLZ!! Convert 80 mph (miles per hour) to feet per second.

Answers

Answer:

117.33333 feet per second

Step-by-step explanation:

Evaluate 10 + 8 ÷ 2 − 4

Answers

Step-by-step explanation:

we will solve this question according to BODMAS rule...

B for bracket

O for of

D for division

M for multiplication

A for addition

S for Subtraction

10+4-4

14-4

10 Answer..

Answer:

10

Step-by-step explanation:

Using order of operations as stated in PEMDAS , that is

division is performed before addition/ subtraction , then

10 + 8 ÷ 2 - 4

= 10 + 4 - 4

= 14 - 4

= 10

Assuming you are creating a book with 549 pages with a size of 8.5in x 11in. how many words will the story be?
A student was conducting a study to determine how many pages he would need for the book he is writing. So, he found that the following number of words fit on each type of the following papers using an 11 point font:

Answers

Answer:

439,200 words

Step-by-step explanation:

800 words per 8.5 inches by 11 inches piece of paper

800 times 549 = 439,200 words

There are 7 blue counters, 3 green counters and 1 red counter in a bag.
There are no other counters in the bag.
Hubert takes at random 2 counters from the bag.
Work out the probability that both counters are blue.

Answers

Answer:

21/55

Step-by-step explanation:

7 blue counters, 3 green counters and 1 red counter  = 11 counters

1st counter

P(blue)= blue / total = 7/11

Now there are only 10 counters

6 blue counters, 3 green counters and 1 red counter  = 10 counters

2nd counter

P(blue)= blue / total = 6/10 = 3/5

P(blue blue) = 7/11 * 3/5 = 21/55

Amanda teaches the art of quilling to 4 students. These students each teach the art of quilling to 4 other students. This process continues through 3 more generations.

Answers

4x4=16 16x3=48 so I think the answer is 48

I'm stuck on here, please, someone help me.

Answers

Answer:

Answer B

Step-by-step explanation:

therw is one full one and one with five

Carrie rolls two 1-6 number cubes. How many outcomes are possible?​

Answers

Answer:

36

Step-by-step explanation:

The first dies has 6 possible outcomes

1,2,3,4,5,6

The second die has 6 possible outcomes

1,2,3,4,5,6

6*6 = 36

There are 36 outcomes

First Sample space

[tex]\\ \sf\longmapsto S=\left\{1,2,3,4,5,6\right\}[/tex]

[tex]\\ \sf\longmapsto |S|=6[/tex]

Now There are two cubes mean n=2

[tex]\\ \sf\longmapsto |S|^n[/tex]

[tex]\\ \sf\longmapsto 6^2[/tex]

[tex]\\ \sf\longmapsto 36[/tex]

The function m is given in three equivalent forms.
Which form most quickly reveals the zeros (or "roots") of the function?
Choose 1 answer:
m(x) = 2(x +4)^2 – 8
m(x)= 2x^2 + 16x + 24
m(x)=2(x+6)(x+2)

Write one of the zeros

Answers

Definitely C, the last one

The product of 2 and a number x is 34.

What is the value of x?


x=54

x=38

x=114

x=32

Pls help me with this guyssss plssss ( I will give brainliest too!) :)

Answers

Answer:

x = 17

Step-by-step explanation:

The product of 2 and a number x is 34 =

2x = 34

x = 34/2

x = 17

Answer:

x=17

Step-by-step explanation:

Product means multiply  is means equals

2x = 34

Divide each side by2

2x/2 = 34/2

x = 17

What is five ones and eight tenths greater than or less than or equal to fifty eight tenths

Answers

Answer:

definetely 2

Step-by-step explanation:

Answer:

Less than

Step-by-step explanation:

Five ones and eight tenths simplifies to 85 and fifty eight tenths simplifies to 580. So, here you can clearly see 85 < 580.

Hope this helps! :)

Problem 2 Find the mBC.

Answers

Answer:

38º

Step-by-step explanation:

<BAC is a central angle. The corresponding arc, BC will be equal to the measure of the central angle.

So mBC = 38º

4.
A turtle crawls 567 mm in 27 minutes. How far (measured in cm) can the turtle
crawl in a minute?

Answers

Answer: 2.1 cm per minute

Step-by-step explanation:

567/27 =21 mm

convert mm to cm (1mm = 0.1c,)

21mm = 2.1cm

Answer:

2.1 cm or 21 mm

Step-by-step explanation:

567 ÷ 27 = 21

Therefore the turtle can crawl 21 mm in a minute.

To covert mm to cm, we simply divide by 10.

21 ÷ 10 = 2.1

Element X is a radioactive isotope such that every 42 years, its mass decreases by
half. Given that the initial mass of a sample of Element X is 50 grams, how long
would it be until the mass of the sample reached 45 grams, to the nearest tenth of a
year?

Answers

Answer:

6.38548 years

Step-by-step explanation:

1 = 2 [tex]e^{42k}[/tex]

1/2 =   [tex]e^{42k}[/tex]

ln(1/2) = 42k ln(e)

ln(1/2)/42 = k

k = -0.01650

~~~~~~~~~~~~~~

45 = 50 [tex]e^{-0.01650t}[/tex]

45/50 =   [tex]e^{-0.01650t}[/tex]

ln(45/50) =  -0.01650 t ln(e)

ln(45/50)/ -0.01650 = t

t = 6.38548 years

The number of years for the radioactive element to reach a mass of 45 grams is given by t = 6.384129 years

What is half-life of an element?

The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.

Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value

The decay constant λ is = 0.693/t½

where t½ is the half-life of the element

Given data ,

Let the number of years be t

Let the initial mass of the element be a = 50 grams

The final mass of the element be ( a - x ) = 45 grams

Now , Element X is a radioactive isotope such that every 42 years, its mass decreases by half

And , half life t½ = 42 years

So , the decay constant k = 0.693/t½

k = 0.693 / ( 42 )

k = 0.0165

And , k= 2.303/t {log (a/a-x)}

So , t = 2.303 / ( 0.0165 ) log ( 50/45 )

On simplifying , we get

t = 6.384129 years

Hence , the number of years for the radioactive element to reach 45 grams is 6.384129 years

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#SPJ2

Please help asap!!!!

Answers

Answer:

1. B,D

2. D

3. C

4. J

Step-by-step explanation:

i need B.

EMERGENCY THANK YOU VERY MUCH!!!

Answers

Answer:

A. Mean = 9.7 (take all the numbers and divide by 10)

Mode = 12

Range = 5

B. Unsure. Would suggest either Mean - average and can tell when bus is running late or early or Mode - highest and lowest time combined

Find the indicated side of the right triangle

Answers

Answer:

Step-by-step explanation:

tan30°=3/x

xtan30°=3

x=3/tan30°

x= 5.2

If the density of the wood is 3 pounds per cubic foot and if the weight of the solid is
360 pounds, what is the width, w, in feet, of the solid?
(A) 5.0
(B) 2.5
(C) 2.4
(D) 1.5

The area of the triangular face of the solid is 48 if that helps

Answers

The width in feet of the given solid is 1.136

Density is defined as the ratio of the mass per unit volume

Density = Mass/Volume

Given

Weight = 360 pounds

Density = 3 pounds per cubic foot

Get the mass;

Since W = mg

m = W/g

m = 360/2.2

m =163.64  lbm/kg

Get the volume

From the formula;

Volume = Mass/Density

Volume = 163.64 /3

Volume = 54.55 ft³

Next is to get the width

Volume of the triangular prism = Base Area * Width

Base Area = 48ft²

54.55 = 48w

w = 54.55/48

w = 1.136

Hence the width of the solid in feet is 1.136ft

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the set is points indicated by 12.is the ___ of the angle

Answers

Answer:

Vertex

Step-by-step explanation:

The vertex is the point were two rays meet to form an angle.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Sally collected 22 pounds of cans to recycle
and plans to collect 1.8 more pounds each
week. In this situation, what is the value of
the y-intercept?

Answers

Step-by-step explanation:

this is an example u can see and write it yourself...

Isabella saved $13,000 and bought a car that cost $11,675. The insurance for the car will cost $650 per year.
How many full years will Isabella be able to pay for car insurance with her remaining savings?

Answers

Answer:

isabella will be able to pay 2 full years of insurance with her remaining savings

Step-by-step explanation:

as we know isabella saved $13,000

the car cost $11,675 - so subtracting that from her total we will know that she has: $1,325 remaining

insurance for a year costs $650,

so we will divide her remaining sum by the yearly cost giving us -

1,325/650

= ‎‎‎2.0.3....

this means that she will be able to pay for 2 full years of insurance with her remaining savings

hope this helped:)

Answer:  2 years

========================================================

Explanation:

x = number of years

Since it costs $650 a year for insurance, she will pay 650x dollars of insurance in total over those x years.

For example, if x = 4, then 650*x = 650*4 = 2600 dollars is paid in insurance.

The expression 650x is added onto the 11675 which is the cost of the car.

Overall, Isabella pays 650x+11675 dollars as the combined cost of the car itself and the insurance over those x years.

Set this equal to 13000 and solve for x

650x+11675 = 13000

650x = 13000 - 11675

650x = 1325

x = 1325/650

x = 2.03846 which is approximate

Rounding down to the nearest whole number gets us to x = 2

She will be able to afford 2 full years of insurance

Note that if x = 3, then,

650x+11675

650*3+11675

13625

Which is 625 dollars over her budget. This shows that she cannot have x = 3 or larger.

Triple a number is 18.

Answers

hi

so 3X = 18

      X = 18/3 = 6

Answer:

6

Step-by-step explanation:

6 + 6 + 6 = 18

1. Eddie ordered customized cups. He was
charged a $30 design fee plus $8 per cup. His
total order was $334. How many cups did Eddie
order?

Answers

Answer:

38 cups

Step-by-step explanation:

8c + 30 = 334

8c = 334 - 30

8c = 304

c = 304 ÷ 8

c = 38 cups

The total number of cups ordered by Eddie is 8

Design fee = $30

Cost per cup = $8

Total cost of order = $334

Let the number of cups ordered = p

The total cost of order can be represented by the equation :

Design cost + (cost per order × Number of orders)

$30 + (8p) = $334

8p = 334 - 30

8p = 304

p = 303 / 8

p = 38

Hence, the number of cups ordered is 8

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Plzzz help 10 points and will mark brainiest
hint: answer is a fraction

Answers

Answer:

1/3

Step-by-step explanation:

The left side of FA is 6 units.

The left side of FB is 2 units.

From 6 to 2, you divide by 3.

Same for the top,

FA is 9 units, while FB is 3 units.

I hope this helps!

pls ❤ and mark brainliest pls!

The lines below are perpendicular. If the slope of the green line is ž, what is
the slope of the red line?
-5
5
m =

Answers

Answer:

B or (-2/3)

Step-by-step explanation:

Perpendicuar lines have negative inverse slopes SO

3/2 ---> -2/3

Can the quotient of two irrational numbers ever be a rational number?

Answers

Answer: Yes, it can.

Step-by-step explanation:

3π / 2π = 1.5

√20 / √5 = 2

I guess it can.

Translate this sentence into a equation. The sum of 22 and chau’s are is 54. Use the variable c to represent chums age

Answers

Answer:

22+c=54

Step-by-step explanation:

22 + his age =54

irrational numbers on a number line pls help!!

Answers

You need to find simple values close to the actual ones asked.

sr(16) = 4 so -sr(17) is slightly below than -4

cr(8) = 2 because 2x2x2=8 so cr(9) is slightly above 2

cr(1) = 1 and cr(8) = 2 so cr(4) is between 1 and 2

Try the others yourself.
-

order the following expressions by their values from least to greatest

Answers

N-Q, N, Q-N

Explanation: N=-2/Q=1
Equations:
-2-1=-3(N-Q)
-2(N)
1- -2=3(Q-N)

The greatest number which on dividing 1657 and 2037 leaves nemainder 6 ands respectively is?​

Answers

Answer:

It would be 127

Step-by-step explanation:

We see that they only have 127 common in their prime factorization. Hence, HCF(1651, 2032) = 127. Hence, the greatest number which divides 1657 and 2037 leaves a remainder of 6 and 5 respectively is 127.

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