4747% of men consider themselves professional baseball fans. you randomly select 10 men and ask each if he considers himself a professional baseball fan. find the probability that the number who consider themselves baseball fans is (a) exactly five, (b) at least six, and (c) less than four.

Answers

Answer 1

Given:
p = 47% = 0.47, the probability that a man considers himself a professional baseball fan.
q = 1 - p = 0.53, the probability that a man does not consider himself a professional baseball fan.
n = 10, the number of men surveyed.

(a) Calculate the probability that exactly 5 of 10 men surveyed consider themselves as professional baseball fans.
P(5 of 10) = ₁₀C₅ p⁵q⁵ = 252*0.47⁵*0.53⁵ = 0.242

Answer: 0.242 or 24.2%

(b) Calculate the probability of at least 6 out of 10.
P(at least 6 of 10)
= ₁₀C₆ p⁶q⁴ + ₁₀C₇ p⁷q³ + ₁₀C₈ p⁸q² + ₁₀C₉ p⁹q + ₁₀C₁₀ p¹⁰ q⁰
= 0.1786 + 0.0905 + 0.0301 + 0.0059 + 0.0
= 0.3057

Answer: 0.3057 or 30.6%

(c) Calculate the probability of less than 4 of 10.
P(less than 4 of 10)
= ₁₀C₁ pq⁹ + ₁₀C₂ p²q⁸ + ₁₀C₃ p³q⁷
= 0.0155 + 0.0619 + 0.1464
= 0.2238

Answer: 0.2238 or 22.4%

Answer 2

The situation represents a binomial probabilty with the probability of success (p) = 47% or 0.47 and the number of trials (n) = 10.

The probability of a binomial distribution is given by:

[tex]P(X)=\left(^n_x)p^x(1-p)^{n-x}[/tex]

Part A:

The probability that the number who consider themselves baseball fans is exactly five is given by:

[tex]P(5)=\left(^{10}_{\,5}\right)(0.47)^5(1-0.47)^{10-5} \\ \\ =252(0.022935)(0.041820)=\bold{0.2417}[/tex]

Part B:

The probability that the number who consider themselves baseball fans is at least six is given by:

[tex]P(X\geq6)=P(6)+P(7)+P(8)+P(9)+p(10) \\ \\ =\left(^{10}_{\,6}\right)(0.47)^6(1-0.47)^{10-6}+\left(^{10}_{\,7}\right)(0.47)^7(1-0.47)^{10-7} \\ +\left(^{10}_{\,8}\right)(0.47)^8(1-0.47)^{10-8}+\left(^{10}_{\,9}\right)(0.47)^9(1-0.47)^{10-9} \\ +\left(^{10}_{10}\right)(0.47)^{10}(1-0.47)^{10-10} \\ \\ =210(0.010779)(0.078905)+120(0.005066)(0.148877) \\ +45(0.002381)(0.2809)+10(0.001119)(0.53)+1(0.000526)(1) \\ \\ =0.1786+0.0905+0.0301+0.0059+0.0005=\bold{0.3056}[/tex]

This can be approximated using normal distribution as I will illustrate in part c.

Part C:

The probability that the number who consider themselves baseball fans is less than four is given by:

[tex]P(X\ \textless \ 4)=P(0)+P(1)+P(2)+P(3)[/tex]

We can approximate this using normal distribution by subtracting 0.5 from the least value and adding 0.5 to the greatest value.

This gives [tex]P(0-0.5\ \textless \ X\ \textless \ 3+0.5)=P(-0.5\ \textless \ X\ \textless \ 3.5)[/tex]

The mean of a binomial distribution is given by [tex]\mu=np[/tex], while the standard deviation is given by [tex]\sigma= \sqrt{np(1-p)} [/tex].

Thus,

[tex]\mu=10(0.47)=4.7 \ and \ \sigma=\sqrt{10(0.47)(0.53)}=1.578[/tex]

The probability of a nomal distribution between two values (a, b) is given by:

[tex]P(a\ \textless \ X\ \textless \ b)=P\left( \frac{b-\mu}{\sigma} \right)-P\left( \frac{a-\mu}{\sigma} \right)[/tex]

Thus,

[tex]P(-0.5\ \textless \ X\ \textless \ 3.5)=P\left( \frac{3.5-4.7}{1.578} \right)-P\left( \frac{-0.5-4.7}{1.578} \right) \\ \\ =P(-0.7605)-P(-3.295)=0.2235-0.0005=\bold{0.223}[/tex]

Related Questions

b) Imagine that you earned $8,425 in one year. If the government enforces a 15% income tax, how much money would you owe in taxes at the end of the year? Show your work.

Answers

$1,263.75 is how much would be taxed
Take 8425 multiply it by 0.15 to get your answer

Answer:

The tax would be $ 1,263.75

Step-by-step explanation:

Given,

Total earning in one year = $ 8,425,

Income tax percentage per year on earning = 15%

Hence, the amount of tax at the end of one year

= 15% of the total earnings

= 15% of 8425

[tex]=\frac{15\times 8425}{100}[/tex]

[tex]=\frac{126375}{100}[/tex]

= $ 1,263.75

Use k as the constant of proportionality to write the equation expressing the relationship: y varies inversely as x.

If y = 25 and k = 50, what is x?

1/2
2
1,250

Answers

y varies inversely as x. this mean x time y = k. We can find x by setting up the equation.

k = xy
Now insert the number we know into the equation. We know y = 25 and k = 50

k = xy
50 = x25
50 = 25x
50 / 25 = 25x/ 25
2 = x
x = 2 <-----answer

Answer: 2

Step-by-step explanation: i got it right :)

How many solutions are there to the following system of equations? Use any method you like, but be sure to show all work.
4x – 14y = 6
–2x + 7y = –3

Please please help! I'm really bad at this! Please show your work so I can understand

Answers

Normally you would expect one solution for x and y, but in this special case, there are an infinite number of solutions because both equations are the same. If you multiply the bottom one with -2, you get:

-2*-2x + -2*7y = -2*-3 simplifies to
4x - 14y = 6, which is the top equation!

If you have one equation with two variables, it is typically not solvable with one set of solutions. x=5 and y=1 is a solution, but so is x=12 and y=3. Those are just two examples.

The areas of: FGHM is 12, MHIJ is 36, EFNL is 24, LNJK is 48. EGIK is a rectangle cut into the rectangles with given areas. What is the area of the shaded quadrilateral EMIN?

Answers

5

Overall area of quadrilateral EGIK is 12+36+24+48 = 120. I'll call the length of EK to be w, and EG to be h, representing width and height.

The line FJ splits EGIK into EFJK and FGIJ which have areas of 72 and 48 respectively. Since EFJK and FGIJ have the width, their heights have to be in the ratio of 72/48 = 3/2. So GF = 2h/5 and EF = 3h/5

Now FGHM and MHIJ share the same height, so their widths have to be in the ratio 12/36 = 1/3, so GH = w/4 and HI = 3w/4

And EFNL and EMIN also share the same height, so their widths have to be in the ratio 24/48 = 1/2, so EL = w/3 and LK = 2w/3.

So the length of MN will be FN - FM. And FN is the same as EL which is w/3, and FM is the same as GH which is w/4. So
w/3 - w/4 = 4w/12 - 3w/12 = w/12

If you look at quadrilateral EMIN, you'll see that it's area is the sum of triangles MNI and MNE. And the area of a triangle is 1/2 bh. And conveniently, we have MN as the base with a length of w/12 for both triangles.

area MNI = 1/2 MN * GF = 1/2 * w/12 * 2h/5 = 2hw/120
area MNE = 1/2 MN * EF = 1/2 * w/12 * 3h/5 = 3hw/120

And their sums are 2hw/120 + 3hw/120 = 5hw/120.
And hw is the total area of EGIK which is 120. So we get:
5 * 120/120 = 5 * 1 = 5

So the area of quadrilateral EMIN is 5.

Area of EMIN = 5 The shaded quadrilateral EMIN is composed of two triangles MNI and MNE. Since the area of a triangle is 1/2bh where b is the base and h the height, the area of the quadrilateral is A = 0.5 * MN * MH + 0.5 MN * EF A = 0.5 MN (MH + EF) Now the large rectangle GIKE has an area of 12+36+24+48 = 120. We'll call the overall width "w" and the overall height "h", so wh = 120. (1) Consider that rectangle GIKE has been divided into 2 rectangles by line FJ. The area above the line is 12+36 = 48, and the area below the line is 24+48 = 72. So the ratio of their heights is 2/3. Therefore we'll call the height of the top rectangle 2h/5 and the bottom rectangle 3h/5. (2) Considering rectangles FGHM and MHIJ, their heights are the same and their areas are in the ratio 12/36=1/3. So we'll consider the width of FGHM to be w/4 and the width of MHIJ to be 3w/4. (3) Now consider rectangles EFNL and LNJK. They also share the same height, so their ratios of width is 24/48 = 1/2. So their widths will be w/3 and 2w/3 respectively. (4) This means that the line segment MN will be w/3 - w/4 = 4w/12 - 3w/12 = w/12 (See (2) and (3) above) Now taking the formula at the very beginning for the area of the quadrilateral EMIN, we have A = 0.5 MN (MH + EF) MN = w/12 ; See (4) above MH = 2h/5 ; See (1) above EF = 3h/5 ; See (1) above So A = 0.5 MN (MH + EF) A = 0.5 w/12 (2h/5 + 3h/5) A = 0.5 w/12 (5h/5) A = 0.5 w/12 h A = w/24 h A = wh/24 And since the overall area of the entire rectangle is wh = 120, we get A = wh/24 A = 120/24 A = 5 As for the actual width and height of the overall rectangle? Don't know and don't care. Any value of w and h will work as long as their product is 120. But regardless of the actual dimensions, the area of quadrilateral EMIN will be 5.

I NEED HELP SOOOO MUCH IM SOOO LOST I WILL GIVE A BRAINLIEST TO THE PERSON WHO INCLUDES ALL WORK, CORRECT ANSWER,AND EVERYTHING MAKES SENSE.

(Variables on both sides of an equation)
Solve: 5(a-1)-15=3(a+2)+4

Answers

5(a-1) - 15 = 3(a+2) + 4
Open all parenthesis and distribute
5a - 5 - 15 = 3a + 6 + 4
Simplify
5a - 20 = 3a + 10
Add both sides by 20 and subtract both sides by 3a
2a = 30
a = 15

We start by using the distributive property to expand the terms [tex]5(a-1)[/tex] and [tex]3(a+2)[/tex]. When we do, we obtain [tex]5a-5[/tex] and [tex]3a+6[/tex].

Putting those back into our equation, we have:

[tex]5a-5-15=3a+6+4[/tex]

Next, we combine all of the constants on either side:

[tex]5a-20=3a+10[/tex]

Finally, we want to get the variable a by itself on one side of the equation, so we perform the following steps to isolate it:

[tex]5a=3a+30[/tex] (Add 20 to both sides)
[tex]2a=30[/tex] (Subtract 3a from both sides)
[tex]a=30/2=15[/tex] (Divide both sides by 2 to isolate a)

So, we obtain our answer of [tex]a=15[/tex].

Loretta and her family are going on vacation. Their destination is 610 miles from their home. Loretta is going to share some of the driving with her dad. Her average speed while driving is 55 mph and her dad's average speed while driving is 65 mph. The plan is for Loretta to drive for this first 4 hours of the trip and her dad to drive for the remainder of the trip

Answers

Loretta:
Average driving speed = 55 mph
Time = 4 hours
Distance traveled = 55*4 = 220 miles

Dad:
Average driving speed = 65 mph
Let x = hours driven
Distance traveled = 65x miles

The length of the trip is 610 miles, therefore
65x + 220 = 610
65x = 390
x = 6 hours

Answer: Loretta's dad drove for 6 hours.

Final answer:

To determine how long Loretta's father drives, we deduct the distance Loretta drives (220 miles) from the total trip distance, then divide the remainder (390 miles) by her father's average speed (65 mph), resulting in 6 hours of driving time for her father. The total trip time is 10 hours.

Explanation:

The question is about calculating travel times and distances using average speed. Loretta and her family are traveling 610 miles with Loretta driving the first 4 hours of the trip at 55 mph and her dad driving the remainder at 65 mph. To calculate the distance Loretta drives, we multiply her driving time by her average speed (4 hours * 55 mph = 220 miles). Then, we subtract that distance from the total trip distance to find out how far her dad drives (610 miles - 220 miles = 390 miles). To calculate how long her dad drives, we divide his driving distance by his average speed (390 miles / 65 mph).

Now let's solve the dad's driving time:
390 miles / 65 mph = 6 hours. So, Loretta's dad would drive for 6 hours. The total driving time for the trip is the sum of both Loretta's time and her dad's time: 4 hours + 6 hours = 10 hours.

For a car rental, the rental agency charges $21.00$⁢21.00 per day, plus $0.23$⁢0.23 for each additional mile above 125125. find a function for the cost of a rental where x is the number of miles driven.

Answers

21d+.23x (d being per day) (x being every mile above 125)

Rita earns $17.00 per hour. If she gets a 6% raise, what will be her new hourly wage?

Answers

multiply 17 by 6%

17 * 0.06 = 1.02 increase

17 +1.02 = 18.02 new hourly wage

You plan to take $450 u.s. on a trip to south africa. how many rands is this if one u.s. dollar equals 3.70 rands?

Answers

$1 = 3.70 rand

$450 is the same as 450 * $1, so multiply both sides of the conversion equation above by 450.

450 * $1 = 450 * 3.70 rand

$450 = 1665 rand

A couch and coffee table cost a total of $1017. The cost of the couch is two times the cost of the coffee table. Find the cost of each item.
cost of couch:
cost of coffee:

Answers

Answer:

Using the concept of linear equations, we made two equations. Solving those two equations, we find that the cost of couch is $678 and that of coffee is $339.

Step-by-step explanation:

Concept: Let the cost of couch be $x and that of coffee be $y. The total cost is $1017, so,

x + y = 1017

Also, the cost of couch is two times that of coffee. So,

x = 2y

Substitute the value of x in first equation

2y + y = 1017

3y = 1017

y = 339

And, x + y = 1017

x + 339 = 1017

x = 678

Using the two equations, we find that y = $339 and x = $678.

So, the cost of couch is $678 and that of coffee is $339.

For more explanation, refer the following link:

https://brainly.com/question/22052132

#SPJ10

What is the percent increase from 42 acres to 72acres

Answers

there is a 71.42857142857143% percent increase you could round that to 71.43%

A number cube is rolled 25 times. A number less than four comes up 20 times. What is the experimental probability that a number less than four is rolled?

Answers

a number less than four came up 20 out of 25 rolls

so the probability was 20/25 which reduces to 4/5

Plz some one help!!!!!!!

Suppose an amount increase by 100%, then decreases by 100%. Find the final amount.Would the situation change if the original increase was 150%? Explain your reasoning.

I will give you 10 points if you help me

Answers

if it increase by 100 and decrease by 100 it would be no difference but if the initial increase was 150 there would be a remainder of 50% of the initial value

Please help me with this

Answers

for an isosceles right triangle the legs would be 2 times the square root of the hypotenuse

so for this:

the legs would be 2sqrt(10)

Which linear function represents the line given by the point-slope equation y + 1 = –3(x – 5)?

Answers

y=-3x+14 I hope this helps!

Answer:

[tex]y=-3x+14[/tex], slope intercept form

[tex]3x+y =14[/tex], standard form

Step-by-step explanation:

[tex]y + 1 = -3(x - 5)[/tex]

We need to write the given equation in slope intercept form or standard form

slope intercept form is [tex]y=mx+b[/tex]

To get slope intercept form , we need to get y alone

[tex]y + 1 = -3(x - 5)[/tex] ( multiply -3 inside the parenthesis )

[tex]y+1=-3x+15[/tex] , subtract 1 on both sides

[tex]y=-3x+14[/tex]

Standard form is [tex]Ax + By = C[/tex]

To get standard form we keep x term and y term on the left hand side

[tex]y=-3x+14[/tex]

Add 3x on both sides

[tex]3x+y =14[/tex]

Help?

Simplify. 9√56x^7y^12 Assume x and y are nonnegative.

Answers

Applying the product property of square roots to the expression 9 * √(56) * √(x^7) * √(y^12), we simplify to 18y^6 * √(14x) * |x^3|.

Apply the product property of square roots:

9 * √(56) * √(x^7) * √(y^12)

Evaluate the square root:

9 * 2 * √(2 * 7) * √(x^7) * √(y^12)

Multiply the numbers:

9 * 2 * √(14) * √(x^7) * √(y^12)

Simplify the square root of an exponential expression:

9 * 2 * √(14) * |x^3| * √(x) * √(y^12)

Simplify the square root of an exponential expression:

9 * 2 * √(14) * √(x) * |x^3| * y^6

Apply the product property of square roots to the product of square roots is equal to the square root of the product:

9 * 2 * y^6 * |x^3| * √(14x)

Multiply the numbers:

18 * y^6 * √(14x) * |x^3|

Describe the transformation.
A) translation 6 units down
B) translation 2 units down
C) reflection across the x-axis
D) reflection across the y-axis

Answers

C) reflection across the x-axis

Answer: C is the answer

Step-by-step explanation:

the quotient of two numbers subtracted from 20

Answers

The quotient of 2 unspecified numbers means division, being x/y - 20. hopefully this helped.

14 minus the product of three and the number has 26

Answers

Assuming “has” means “equals”

14 - 3 (x) = 26
Subtract 14 from both sides
-3x = 12
Divide both sides by -3
X= -4

Help me solve this plzz!!Simplify:

Answers

a.

You can use the rule:
[tex](a^b)^c=a^{b*c} [/tex]

So, let's do it:
[tex](27x^6)^ \frac{1}{3} = 27 x^{6* \frac{1}{3} } [/tex]

Simplify:
[tex](27x)^2[/tex]

And there you have it. If you need it one step further, then square 27, but take the parenthesis out.

If you need further help, feel free to ask for it.

In a dilation, the ratio of the length of a side on the image to the length of its corresponding side on the pre-image is called the __________ __________.

A. center of dilation
B. scale factor
C. mapping rule
D. expansion or contraction

Answers

B scale factor
that shuld b d answer

Light travels 9.45 \cdot 10^{15}9.45⋅10 15 9, point, 45, dot, 10, start superscript, 15, end superscript meters in a year. there are about 3.15 \cdot 10^73.15⋅10 7 3, point, 15, dot, 10, start superscript, 7, end superscript seconds in a year. how far does light travel per second?

Answers

We are given that the distance light travel is:

9.45 x 10^15 meters / year

And that there is:

3.15 x 10^7 seconds / year

So the distance light travels per second is:

distance = (9.45 x 10^15 meters / year) * (1 year / 3.15 x 10^7 seconds)

distance = 3 x 10^8 meters / second

The distance of the light travel per second is 3 x 10^8 meters/second

We are given that the distance light travel is

9.45 x 10^15 meters / year

And that there is

3.15 x 10^7 seconds / year

So the distance light travels per second is:

What is the distance light travels per second?

It is defined as the distance that light travels in free space in one second.

Therefore we get,

distance = (9.45 x 10^15 meters / year) * (1 year / 3.15 x 10^7 seconds)

distance = 3 x 10^8 meters / second.

Therefore the distance of the light is 3 x 10^8 meters/second.

To learn more about the distance of the light visit:

https://brainly.com/question/9624014#SPJ3

Anna has 5 muffins but 8 friends coming over. How much will each friend get

Answers

Hello! To solve this question, all we have to do is 5/8. You can basically leave it like it is, because that’s your answer. Each friend will get 5/8 of a muffin.

In a study, the sample is chosen by writing everyones name on a playing card, shuffling the deck, then choosing the top 20 cards what is the sampling method

Answers

Random sampling because everyone has an equal chance

Simple random sampling is much better than others because it saves time and it is the most reliable method of obtaining information where every single member of the population is chosen randomly. or by chance. Each has an equal chance to be selected.

Sampling

It is a process applied in statistical analysis in which a predetermined number of observations is taken from a large population.

Given

The sample is chosen by writing everyone's name on a playing card, shuffling the deck, then choosing the top 20 cards.

To find

The sampling method for this condition.

How to choose the sampling method?

So, simple random sampling is much better than others because it saves time and it is the most reliable method of obtaining information where every single member of the population is chosen randomly. or by chance. Each has an equal chance to be selected.

More about the sampling link is given below.

https://brainly.com/question/350477

Liz wants to buy a shirt for $25. How much will Liz's shirt cost in Springfield(4.1%) Round up to the nearest cent? Show your work

Answers

In order to find the total amount of the shirt including tax, first convert the tax into a decimal:
4.1/100 = 0.041 %
Next multiply the cost of the shirt before tax by the tax in decimal form:
25 * 0.041 = 1.025
After that you will add the tax cost and the shirt cost:
25 + 1.025 = 26.025
Finally round to the nearest cent:
26.03
Hope this helps and let me know if you have more questions!

I think it would be $102.6

Choose all of the following relationships that represent functions. please help!!

Answers

The rule of a function is:
You CANNOT have one x-value with multiple different y values in the same function. You can however have different x values with the same y value.
Also for reference: independent means x value and dependent means y- value.

The first answer is not a function because as you can see there is one x-value with multiple y values.

second answer IS a function because as I said before you can have different x values with the same y value

third answer is a function again because you can have different x values with same y value

number four isn't a function bc again the -2 x value has 2 different y Values.

The answers are B and C

PLEASE ANSWER WORTH 99 POINTS

Each serving of a cereal is 80 calories. Which expression can be used to find the number of calories in 3 servings?
80 x 3
80 divided by 3
3 divided by 80
80 - 3

Answers

B. 80 x 3 if it is three times you would put 80 in three times or just multiply it by 3

80(3)=240
80/3=26.66
3/80=0.0375
80-3=77

State the vertex as an ordered pair.

y = -|3x +5|+7

Answers

in plain and short, what value of "x" makes the expression |3x + 5| to 0?

well, we can check by simply setting it to 0 and solving for x.

[tex]\bf 3x+5=0\implies 3x=-5\implies \boxed{x=-\cfrac{5}{3}}\\\\ -------------------------------\\\\ \textit{therefore, the vertex of }y = -|3x+5|\boxed{+7}\textit{ is at }\left(-\frac{5}{3}~,~7 \right)[/tex]

notice, all you do is, get the x-value that makes the expression to 0, and then append the constant outside it as the y-value, and that's the vertex.

The perimeter of a triangle is 29 feet where one side of the triangle is twice the length of the shortest side. the largest side is 13 feet more than the shortest side. how long is the shortest side

Answers

x + 2x + (13 + x) = 29
3x + x + 13 = 29
4x = 29 - 13
4x = 16
x = 16/4
x = 4

The length of the shortest side is 4 ft

Answer:

The shortest side is 4 feet.

Step-by-step explanation:

The perimeter is the border of a geometric figure and corresponds to the sum of the length of all its sides.

So the perimeter in the case of a triangle is the sum of its three sides:

L₁ + L₂ + L₃ =Perimeter

In this case, the perimeter is known and it is necessary to calculate the value of the shortest side. In that case it will be called L₁. So, you know:

L₁= shortest sideL₂=twice the length of the shortest side → L₂=2*L₁L₃=largest side (13 feet more than the shortest side) → L₃=L₁ + 13Perimeter= 29 feet

Replacing:

L₁ + 2*L₁ + L₁ + 13= 29

Solving:

(1+2+1)*L₁ + 13= 29

4*L₁ + 13=29

4*L₁ = 29-13

4*L₁ =16

L₁= 16÷4

L₁=4

The shortest side is 4 feet.

Use laws of sine to answer

Answers

By sine rule:
[tex] \frac{18}{ \sin(32) } = \frac{bc}{ \sin(118) } [/tex]
so:
[tex]bc = \frac{18 \times \sin(118) }{ \sin(32) } \\ bc = 29.991... \\ bc = 30.0 \: (to \: 3 \: sig.figs)[/tex]

Other Questions

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