Exercise: 6.68 'Cat Owners': According to the American Veterinary Medical Association, 30% of Americans own a cat. Find the probability that exactly 2 out of 8 randomly selected ­Americans own a cat. In a random sample of 8 Americans, find the probability that more than 3 own a cat.

Answers

Answer 1

Using the binomial distribution, it is found that there is a:

0.2965 = 29.65% probability that exactly 2 out of 8 randomly selected ­Americans own a cat.0.4482 = 44.82% probability that more than 3 own a cat.

What is the binomial distribution formula?

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.

In this problem, we have that:

30% of Americans own a cat, hence p = 0.3.A sample of 8 Americans is taken, hence n = 8.

The probability that exactly 2 out of 8 randomly selected ­Americans own a cat is P(X = 2), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{8,2}.(0.3)^{2}.(0.7)^{6} = 0.2965[/tex]

0.2965 = 29.65% probability that exactly 2 out of 8 randomly selected ­Americans own a cat.

The probability that more than 3 own a cat is given by:

[tex]P(X > 3) = 1 - P(X \leq 2)[/tex]

In which:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

Hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{8,0}.(0.3)^{0}.(0.7)^{8} = 0.0576[/tex]

[tex]P(X = 1) = C_{8,1}.(0.3)^{1}.(0.7)^{7} = 0.1977[/tex]

[tex]P(X = 2) = C_{8,2}.(0.3)^{2}.(0.7)^{6} = 0.2965[/tex]

Then:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0576 + 0.1977 + 0.2965 = 0.5518[/tex]

[tex]P(X > 3) = 1 - P(X \leq 2) = 1 - 0.5518 = 0.4482[/tex]

0.4482 = 44.82% probability that more than 3 own a cat.

More can be learned about the binomial distribution at https://brainly.com/question/24863377


Related Questions

Susan has a collection of 44 nickels and dimes. If the number of nickels is three times the number of​ dimes, how many nickels and how many dimes does she​ have?

Answers

Answer:

33 nickels and 11 dimes

Step-by-step explanation:

11*3= 33

11 + 33 = 44

PLEASE HELP ME WILL GIVE BRAINLIEST

Answers

Answer:

1 3/4, 0

Step-by-step explanation:

You have to go 1 3/4 to the right and 0 up.

Reflect the given triangle over
the x-axis.
[_
3 6 31
-3 3 3.
3 [?]
13
UD
[

Answers

[3 6 3]

( 3 3. 3]

THIS ANSWER IS CORRECT

Solution:

[tex]\sf \left[\begin{array}{ccc}3&6&3\\3&-3&-3\end{array}\right][/tex]

Explanation:

[tex]\sf \left[\begin{array}{ccc}3&6&3\\-3&3&3\\\end{array}\right][/tex]

The rule for a reflection over the x -axis is (x,y) → (x,−y)

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

or multiply the matrix with:      [tex]\left[\begin{array}{ccc}1&0\\0&-1\end{array}\right][/tex]

[tex]\dashrightarrow \ \sf \begin{pmatrix}1\cdot \:3+0\cdot \left(-3\right)&1\cdot \:6+0\cdot \:3&1\cdot \:3+0\cdot \:3\\ 0\cdot \:3+\left(-1\right)\left(-3\right)&0\cdot \:6+\left(-1\right)\cdot \:3&0\cdot \:3+\left(-1\right)\cdot \:3\end{pmatrix}[/tex]

Final answer:

[tex]\sf \left[\begin{array}{ccc}3&6&3\\3&-3&-3\end{array}\right][/tex]

please help! What is 75 % of 62-(98/4)

Answers

Answer:

28.13

Step-by-step explanation:

62 - (98/4)

62 - 24.5 = 37.5

75% of 37.5 is 28.125, or 28.13.

Answer:

22

Step-by-step explanation:

98/4 = 24.5

62-24.5 = 37.5

75% of 37.5

= about 22

Carly is in charge of bringing juice for the class party. Her class has 24 students and 1 teacher. She estimates that each person will drink 400 milliliters of juice. To make sure she has enough, she also wants to bring an extra liter of juice. How many liters of juice should Carly bring in all?

Answers

Answer:

10,000

Step-by-step explanation:

if it's including the teacher then it should be 10,000

Single post math redo question

Answers

Answer:

See attached graph

Step-by-step explanation:

We need to convert the polar coordinates into Cartesian coordinates using the rules [tex]x=r\:cos\theta[/tex] and [tex]y=r\:sin\theta[/tex] (see table in attached file).

The converted points will start to resemble a circle with a horizontal pole and a diameter of 4, so by connecting the points, we get our equation [tex]r=4\:cos\theta[/tex].

Can anyone help me on this question?

Answers

n= 35 because 145x2=290. That leaves 70 left for 360 and you divide 70 by 2 to get 35. So, n is 35


Find the equation of the tangent to the circle x2 + y2 = 109 at point (-10,3)

Answers

Answer:

10x - 3y = -109 .

Step-by-step explanation:

x^2 + y^2 = 109

Implicit Differentiation:

2x + 2y.y' = 0

y' = -2x/2y = -x/y

So at the point (-10,3) the gradient of the tangent is -(-10)/3 = 10/3.

Equation of the tangent:

y - y1 = m(x - x1)

y - 3 = 10/3(x + 10)

y - 3 = 10/3 x + 100/3

3y - 9 = 10x + 100

-109 + 3y = 10x

10x - 3y = -109  

A trough contains a certain amount of sand. After Jamie used it to fill 2.4-kilogram bag, a 650- gram bowl, and a 3-kilogram, 125- gram pail, she realized she had a kilogram of sand left in the trough. How much sand was in the trough at first?Give your answer in grams, using a comma.

Explain how you got your answer

Answers

Answer:

7kg  275g

Step-by-step explanation:

hope this helps

Answer:

7kg 275g

Step-by-step explanation:

Add all of them together and then add what's left. Hope this helps! :)

Carl is arranging 86 chairs for a
dinner party. Carl places 5 chairs at
each table. Any remaining chairs will
be set aside. How many tables will
have 5 chairs?

Answers

||17 tables|| will have 5 chairs because 86 divided by 5 is 17.2 so 17 tables with 5 in total


The digits 5, 7, 1, and 9 are to be used in a roll number in a school. How
many different roll numbers are possible if repetitions are not permitted?

Answers

Answer:

1, 7, 5, 9
7, 1, 9, 5

9, 5, 1, 7

But there are about 10 possible combinations.

Step-by-step explanation:

If y varies inversely as x, and y=16 when x=4, find y when x=10

Answers

Answer:

40

Step-by-step explanation:

you have to multiply x by 4 to get y when x=4 and y=16. so if x=10, then you have to multiply what x is (10) by 4 because there is a common ratio.

hope this helps!! please give brainliest!!!!!!

hi there im giving brainliest to the most accurate answer.

Answers

Triangle b and c by AAA axiom because all angles are equal

arrange in descending order​

Answers

Answer:

7 / 16, 3 / 7, 1 / 5

Step-by-step explanation:

1 / 5 = 0.2

3 / 7 = 0.428

7 / 16 = 0.4375

In descending order,

0.4375, 0.428, 0.2

Hence the answer is 7 / 16, 3 / 7, 1 / 5

Answer:
7/16,3/7.1/5
Step-by-step explanation:
1/5 = 0.2
3/7= 0.428
7/16 = 0.4375
In descending order,
0.4375, 0.428. 0.2

Which fraction equals 29 }}16 ?

Answers

For 29/16, the denominator is 16. Improper fraction. This is a fraction where the numerator is greater than the denominator. Mixed number

f(x)=−2x+3; Domain: {−1,0,2}

Find the range of the function for the given domain.

Answers

Answer:

Range: 1,3,7

Step-by-step explanation:

(-1,1),(0,3),(2,7)

2(-1)+3

2(0)+3

2(2)+3

What is the outlier for the data set? PLS HELP I REALLY NEED HELP :(
Heart Rate
5 0 7
6 3 5 6 8 8
7 0 2
8
9 0
5 0 = 50 beats per minute
40
50
68
90

Answers

Answer:

6 3 5 6 8 8

Step-by-step explanation:

number is farthest apart from others

Answer:

The correct answer is 90

Step-by-step explanation:

90 is the biggest number in the number set so therefore it is an outlier.

Have an amazing day!!

Please rate and mark brainliest!!

You need 3 sticks of butter for every 24 giant cookies you bake.

Answers

Answer:

Sticks of butter : 2

Number of cookies : 40

Step-by-step explanation:

Given that :You need 3 sticks of butter for every 24 giant cookies you bake.

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

Sticks of butter                    Number of cookies

 3                                           24

 x                                             16

5                                                 y

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

Let the unknown be x and y..

Since you need 3 sticks of butter for every 24 giant cookies you back

Then 24/3 = 8

Since the number of cookies is 16 then 16/8 = 2

Thus x = 2

Next for y.

Since you need 3 sticks of butter for every 24 giant cookies you back

Then 5 * 8 = 40

Thus, y = 40

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

Completed table below:

Sticks of butter                    Number of cookies

 3                                           24

 2                                             16

5                                                 40

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

~lenvy~

Answer:

See below ↓

Step-by-step explanation:

Given

You need 3 sticks of butter for every 24 cookies

Base rate

no. of butter sticks / no. of cookies3 / 241 stick of butter for every 8 cookies

16 cookies

No. of sticks = 16/8No. of butter sticks = 2

5 butter sticks

No. of cookies = 8 x 5No. of cookies = 40

jill has a small treasure box

Answers

jill has a small treasure box
=small treasure box in possession of jill

The area of a rectangular field is 1.12×10^45 square feet. If the length of the field is 7×10^11 feet, and the width of the field can be written as 1.6×10x feet, what is the value of x?

Answers

Answer:

x = 10^34

Step-by-step explanation:

length × width = area

area/length = width

width = (1.12 × 10^45 ft²)/(7 × 10^11 ft)

width = 1.12/7 × (10^45)/(10^11)   ft

width = 0.16 × 10^34  ft

width = 1.6 × 10^34  ft

width = 1.6 × x  ft

x = 10^34

The value of x is [tex]10^3^2[/tex]  or [tex]\rm x =10^3^2[/tex]

It is given that the area of a rectangular field is  [tex]\rm 1.12\times10^4^5 \ feet^2[/tex]

It is required to find the value of x

What is the area of the rectangle?

It is defined as the space occupied by the rectangle which is planner 2-dimensional geometry.

The formula for finding the area of a rectangle is given by:

Area of rectangle = length × width

We have:

Area of rectangle = [tex]\rm 1.12\times10^4^5 \ feet^2[/tex]

The length of the rectangle = [tex]7\times 10^1^1[/tex] feet

The width of the rectangle = [tex]\rm 1.6\times 10x[/tex] feet

After putting the values in the formula, we get:

[tex]\rm 1.12\times10^4^5 =7\times 10^1^1\times\rm 1.6\times 10x[/tex]

[tex]\rm x =\frac{1.12\times10^4^5}{7\times 10^1^1\times\rm 1.6\times 10} \\[/tex]

[tex]\rm x =\frac{1.12\times10^4^5}{7\times 10^1^1\times\rm 1.6\times 10} \\\\\rm x = 0.1\times 10^3^3[/tex]

[tex]\rm x =10^3^2[/tex]

Thus, the value of x is [tex]10^3^2[/tex]

Learn more about the area here:

https://brainly.com/question/14383947

Please help i really dont like iready and im really confused. thank you!

Answers

Answer:

15 inches cubed

Step-by-step explanation:

length 2 1/2 in

width 1 1/2 in

height 4 in

V= = l x w x h

V = 2 1/2 x 1 1/2 x 4

60/4 = 15

HELLPPPP REALLLLYYY NEEDDD
THISS ANSWER

Answers

Answer:

we need a picture to help

Step-by-step explanation:

Answer:

what is the question man stop messing around

The price of a used car that Billy is buying is $5,000. If he has to pay 8% in taxes, how much will be have to pay for the car including taxes?

Answers

Answer:

5400

Step-by-step explanation:

8% of 5000 is 400. 5000 + 400 - 5400.

Answer:

$5400

Step-by-step explanation:

We need to find the amount of tax in $

So, if 100% = $5000

           8%   =  ?

cross multiply to be :  8 × 5000

                                        100

to get $400

Add it to the $5000 to get $5400

Suppose that two cards are randomly selected from a standard​ 52-card deck.
​(a) What is the probability that the first card is a spade and the second card is a spade if the sampling is done without​ replacement?
​(b) What is the probability that the first card is a spade and the second card is a spade if the sampling is done with​ replacement?

Answers

Answer:

A) 4 of the 52 cards are queens on the first draw; 3 of the remaining 51 cards are queens on the second draw: (4/52)*(3/51)

B) 4 of the 52 cards are queens on each draw: (4/52)*(4/52)

Step-by-step explanation:

correct me if. wrong

The quotient of w and 7 is less than 17.

Answers

Answer:

17 < w / 7 is my answer. I am not sure to correct.

Find the area of the triangle.
16 ft
20 ft


Please help

Answers

The answers would be 320ft. Squared
Assuming 16 is the length and 20 is the width the answer would be 160 because the equation for the area of a triangle is ((l x w) / 2)

If it’s 1 pm what time will it be in 30 hours

Answers

Answer:

7pm

Step-by-step explanation:

1pm + 24 = 1pm

30 - 24. = 6

1pm + 6 = 7pm

NOW I NEED HELP NOW PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS

Mya is redecorating her bedroom. The room is in the shape of right rectangular prism.

The dimensions of the room are: 12 feet in length by 14 feet in width by 8 feet in height.

She plans to cover the floor with tile. The cost of the tile is $4 per square foot.

She plans to cover the walls and the ceiling with paint. Each container of paint costs $16 and can cover 146 ft².

What is the total cost of the tile flooring and paint needed for this room?

Drag and drop the responses to correctly complete these sentences.

The total square feet of flooring needed is ____ and the flooring cost will be ____

The total square feet that will need to be painted is ____ and the paint cost will be ____

The total cost of the tile flooring and paint needed for this room is ____

Answers

Answer: took the test and the answers are at the bottom. cheers mate :)

Step-by-step explanation:

Kyle lives in a state that has a 6% (or 0.06) sales tax. If c represents the cost of an item and t represents the sales tax on the item, which equation expresses the relationship between these two variables?
Group of answer choices

t = 6c

t = 0.6c

t = 0.06c

t = c + 0.06

Answers

Answer:

The answer is the 3rd option

t = 0.06c

Answer:

t = 0.06c

Step-by-step explanation:

What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.

Answers

Answer:13.1

Step-by-step explanation:

Area equation:S=[tex]S=\frac{1}{2} ab sinθ[/tex]

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