At a new exhibit in the Museum of Science, people are asked to choose between 94 or 220 random draws from a machine. The machine is known to have 99 green balls and 78 red balls. After each draw, the color of the ball is noted and the ball is put back for the next draw. You win a prize if more than 61% of the draws result in a green ball. a. Calculate the probability of getting more than 61% green balls.

Answers

Answer 1

Answer:

0.0869 = 8.69% probability of getting more than 61% green balls.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

The machine is known to have 99 green balls and 78 red balls.

This means that [tex]p = \frac{99}{99+78} = 0.5593[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.5593[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.5593*0.4407}{99+78}} = 0.0373[/tex]

a. Calculate the probability of getting more than 61% green balls.

This is 1 subtracted by the pvalue of Z when X = 0.61. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.61 - 0.5593}{0.0373}[/tex]

[tex]Z = 1.36[/tex]

[tex]Z = 1.36[/tex] has a pvalue of 0.9131

1 - 0.9131 = 0.0869

0.0869 = 8.69% probability of getting more than 61% green balls.


Related Questions

my points is going lower and lower and lower and lower until its zero

But i dont care.




Just answer my question in the picture above. ​

Answers

Answer:

c, a, b

...................

Joyce determines that 30% of her monthly income goes for rent. If her monthly income is $2,009, about how much is her monthly rent? How much is her yearly rent?

Answers

Answer:

602.7

7,232.4

Step-by-step explanation:

2009 x 0.30 = 602.7

602.7 x 12 = 7232.4

A study of drive-thru wait times for fast-food restaurants found that the average time spent Wendy's drive-thru was 138.5 seconds. Assume that drive-thru wait times are normally distributed with a standard deviation of 29 seconds, A Wendy's owner wants to give a free Frosty to customers who have an unusually long wait in the drive-thru.
The length of time the owner should choose so that only 0.75% of customers get a free Frosty i.e. only 0.75% wait longer than ________ seconds) is _________ seconds (give your answer to 2 decimal places).

Answers

Answer:

207.72 seconds.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean waiting time of 138.5 seconds, standard deviation of 29 seconds.

This means that [tex]\mu = 138.5, \sigma = 29[/tex]

The length of time the owner should choose so that only 0.75% of customers get a free Frosty i.e. only 0.75% wait longer than

The 100 - 0.75 = 99.15th percentile, which is X when Z has a pvalue of 0.9915, so X when Z = 2.387.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]2.387 = \frac{X - 138.5}{29}[/tex]

[tex]X - 138.5 = 2.387*29[/tex]

[tex]X = 207.72[/tex]

So the answer is 207.72 seconds.

Which one was the answer A,B,C or D?

Answers

Answer:

A

Step-by-step explanation:

A answer is a

step by step

On weekends, Ben mops the kitchen floor. Below is an image that shows
the dimensions of the floor, in feet.
10
4
8
4
Question: What is the the total area of the kitchen floor?

Answers

I’m pretty sure it’s 24

w
The table below lists the means and standard deviations for 5th graders in the district and for the norm group for
student performance in four different subjects. According to the table, the performance of the 5th graders in the
district is more variable than that of the norm group in which subject(s)?
ed
ati
n
100
Sc
Geography English Spelling Science
Mean of all 5th graders in District (150 students) 75
125 90
SD of these 5th graders
12
10 12 20
Mean of the Norm Group
85
100 120 90
SD of the Nom Group
10
10 15 15
ww
sti
20
ker
ndo
ted
Geography, Spelling, and Science
Geography and Spelling
Geography and Science
Spelling only
Science only
Geography only
lccr
Sa
le au
isid

Answers

Answer:

Can you please format this? it's hard to understand right now

search correct answer which expression is equivalent to the polynomial?​

Answers

Looks like C due to the exponent outside the parenthesis

If it is wrong I apologize and hope this bobcat will make it better

A rocket is fired directly upwards with a velocity of 80 ft/sec. The equation for its height, H, as a function of time, t, is
given by the function
H (t) = -1612 + 80+
Find the time at which the rocket reaches its maximum height, and its maximum height.
5
a) O time =
22
sec, max height = 200 ft
b) O time = 80 sec, max height = 100 ft
5
c) O time =
2
sec, max height = 100 ft
d) O time = 5 sec, max height = 200 ft
5
e) Otime = sec, max height = 400 ft
23
Revie

Answers

Answer:

(c).

Step-by-step explanation:

h(t) = - 16 t² + 80 t

Coordinates of the vertex are:

t = - [tex]\frac{80}{2(-16)}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5 sec.

h = - 16(2.5)² + 80(2.5) = - 100 + 200 = 100 ft.

Find the missing side. Round to the nearest tenth.

Answers

Answer:

Step-by-step explanation:

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

1)

Hyp =40

∠48

x = Adj

use CAH since it's got these pieces in it

Cos(48) = x / 40

40* Cos(48) = x

26.76522 = x

x = 26.8  ( rounded to nearest 10th)

2)

∠29

Hyp = 35

Opp = x

use SOH since this problem has those pieces in it

Sin(29) = x / 35

35*Sin(29) = x

16.9683 = x

x = 17.0  (rounded to nearest 10th)

3)

40 = Adj

∠16

Hyp = x

use CAH again

Cos(16) = 40 / x

x = 40 / Cos(16)

x = 41.611

x = 41.6 (rounded to nearest 10th )

4)

∠55

Opp = 35

x = Adj

use TOA

Tan(55) =35/x

x = 35/Tan(55)

x = 24.5072

X = 24.5  ( rounded to nearest 10th)

Why do you think we need to convert normal distribution to standard normal distribution?

Answers

Answer:

The standard score (more commonly referred to as a z-score) is a very useful statistic because it (a) allows us to calculate the probability of a score occurring within our normal distribution and (b) enables us to compare two scores that are from different normal distributions

7. In the figure, AABC-AXYZ. What is the perimeter of AABC? Show your work.

Answers

The answer would be 36

Rosaria filled some cups with different amounts of water, as shown below.Red cup: 0.046 liters
Blue cup: 0.05 liters
Green cup: 0.20 liters
Yellow cup: 0.6 liters witch one

Answers

Answer:

Green cup: 0.20 liters

Step-by-step explanation:

Nicole took a taxi from her house to the airport. The taxi company charged a pick-up
fee of $2.90 plus $1.75 per mile. The total fare was $44.90, not including the tip.
Write and solve an equation which can be used to determine z, the number of miles
in the taxi ride

Answers

Answer: 2.90 + 1.75z = 44.90
z = 24 miles
Steps:
2.90 + 1.75z = 44.90
1.75z = 44.90 - 2.90
1.75z = 42
z = 42/1.75
z = 24

Check:
2.90 + 1.75z = 44.90
2.90 + 1.75(24) = 44.90
2.90 + 42 = 44.90
44.90 = 45.90 ✅

I would appreciate the brainliest if this was helpful correct and had clear steps! :)

The first thing we need to do is to find the linear equation that defines the total cost of the taxi ride as a function of the number of miles traveled.

We will find that z = 24.

We know that the taxi charges a fixed fee of $2.90, plus $1.75 per mile.

So if you travel for z miles, the total cost will be:

[tex]c(z) = \$2.90 + \$1.75 \cdot z[/tex]

Now that we have this linear equation if we know that the total fare was $44.90, then we have:

[tex]c(z) = \$2.90 + \$1.75 \cdot z = \$44.90[/tex]

Now we just need to solve the above equation for z:

[tex]\$2.90 + \$1.75 \cdot z = \$44.90\\\\\$1.75 \cdot z = \$44.90 - \$2.90 = \$42.00\\\\z = \$42.00/\$1.75 = 24[/tex]

Then we can see that she traveled for 24 miles.

If you want to learn more, you can read:

https://brainly.com/question/19770987

One year, the population of a city was 189,000. Several years later it was 223,020. Find the percent increase.

Answers

Answer:

18%

Step-by-step explanation:

Find the area of sector with a radius of 4 and a central angle of 30 degrees.

Answers

Answer:

Step-by-step explanation:

[angle of sector]/360 x π x radius ² [formula to find area of a sector]

30/360 x π x 4²

Type into a calculator

4.18879

I NEED HELP FAST! Which of the following sets of numbers could not represent the three sides of a triangle?

Answers

Answer:

(8, 23, 31)

Step-by-step explanation:

The sum of the lengths of the two shorter legs must be greater than the length of the longer leg

(not equal to either)

find the product (ab-3)^2

Answers

Answer:

a^2b^2 -6ab + 9

Step-by-step explanation:

There are 20 pieces of fruit in a basket and 12 of them are oranges. What percentage of the pieces of fruit in the basket are oranges? Show your work in the box and circle your answer

Answers

Answer:60 percent

Step-by-step explanation: You have fraction the two numbers which will be 12/20 them you times it by 100 which equals 60 oranges.

The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method. y2 − x2 = 4, y = 3; about the x-axis

Answers

Step-by-step explanation:

it actually equals 3 you x=+_√7 buy washing method

4. Tori bought x shares of Mattel stock for m dollars per share. She sold
all of the shares months later for y dollars per share. Express her cap-
ital gain or loss algebraically.

Answers

Answer:

mx = y

or

y = mx

Step-by-step explanation:

If she pays m per share, and x represents each share, you will multiply m and x. If she sold all them for the value of y. Then you set mx equal to y.

mx = y

or

y = mx

What is the degree of the following polynomial x²y³ + z



Answers

The answer on top of me is correct

To decorate 6 dozen cupcakes with red hot candies, Nan needs about 550 red hots. Which two sacks of candy would be the best buy?plsss help me asap giving brainless and explain whay is that the answer.​ (353, 177, 255, 379)​

Answers

Answer:

If the numbers at the bottom are the sack size, then the 255 and the 353.

They give enough candy but not excessive given the sizes.

If this isn't right I will continue to try to help you but ill need more info

(40 POINTS!!) solve for x

Answers

Answer:

do 13+7 you will have your answer. (go down for answer)

Step-by-step explanation:

its 20

What does 3 to the power of 2 minus 4 times 2 plus 6

Answers

Answer:

7 is the answer

Step-by-step explanation:

Answer:

This equals 7

Step-by-step explanation:

I used a calculator

Can I have brainliest pls

Find the value of x and y. This has to do with geometry

Answers

Answer:

x = 30°

y = 30°

Step-by-step explanation:

By inscribed angle theorem:

[tex]x = y = \frac{1}{2} \times 60 \degree \\ \\ x = y = 30 \degree[/tex]

ASAP I WILL GIVE BRAINIEST IF ANSWERED ASAP!! PLEASE PLEASE HELP

Answers

Answer:

2x + 3 =84

Step-by-step explanation:

Answer:

2x + 3 = 84

Step-by-step explanation:

-3 + 8n = -5
what is n?

Answers

click link above for the answer

Answer:

-1/4

Step-by-step explanation:

55 people showed up on a party.There were 3 less women than men.how many men were there?​

Answers

Answer:

52

Step-by-step explanation:

55 - 3 = 52

give me brainiest wink wink

29 men

Set up a system of equations. If w is the number of women and m is the number of men, we know that w+m=55, and that w=m-3. If you solve this, you get that m-3+m=55 → m=29.

The variable z varies jointly with x and y. Also, z = -75 when x = 3 and y = -5.

What equation describes this variation?

x = kyz
y = kxz
z = kxy
k = xyz

Answers

What equation describes this variation?

z = kxy

What is the constant of variation?

k = 5

When x = 1 and y = –2, z =

-10

Step by Step Explanation:

With the equation z = kxy and the values for z, x, and y, we can find k.

z = kxy

-75 = (k) (3) (-5)

-75 = (k) (-15)

5 = k

k = 5 (final answer).

To check our work, we just enter all of the values and make sure it adds up.

z = kxy

-75 = (5)(3)(-5)

-75 = 15(-5)

-75 = -75

correct!

Do the same to find the answer for the next part to get -10.

Further proof in the file attached.

Answer:

C.

5

-10

NEXT SLIDE:

3/8

3/40

NEXT SLIDE:

A.

7

42

NEXT SLIDE:

D.

6

NEXT SLIDE:

B.

10

LAST SLIDE:

A.

D.

Step-by-step explanation:

100% Edge 2021

I did the Assignment.

Good luck catching up in Edge before the end date fam!

CAN ANYONE PLEASE HELP ME?.......

Find P(4).

A. 1/8
B. 1/4
C. 1/2​

Answers

It’s C because I got an A on that quiz and it was pretty hard

Answer:

A. 1/8

Step-by-step explanation:

n(4) = 1

n(S) = 8

p(4)= n(4)/n(S)

=1/8 Ans.

Other Questions
While the Bourbon Triumvirate did want to strengthen economic ties with the North, unfortunately, they also wanted to keep some of the traditions of the Old South, like white supremacy. Ture or Falsw Why did Enrique choose to travel alone and not inform others about his journey What is the measure of angle GXI? The area of a trapezoid is 60 square feet the bases of the trapezoid are 8 feet and 12 feet, what is the height?6ft4ft3ft15ft Why is this question stumping everyone i meet. can you help me find the slope of these queastions? which statement is true. WHAT IS THISSSSSSSSSSSSS 2. A local t-shirt company sold 2000 t-shirts two weeks ago when they charged $10 for each shirt. The following week they sold 1120 t-shirts when they raised the price to $19 per shirt. Assuming that this rate of change continues find the following: a. Find a linear function S(p) that models the number of shirts sold as a function of the price p. b. Explain the meaning of the slope In terms of the problem. c. Predict the number of shirts the store would sell if they charged $25 for each shirt. d. If the store would like to maintain a weekly sales level of 1450 shirts how much should they charge per shirt? How did Abolitionists work to end American Slavery? Which of the following are logical reasons for using a pie chart to show how employees spend their time at ABC organization? Choose all that apply. HELP!!!! WILL MARK BWhich of the following leaders led Athens for 30 years and supported writers, teachers, as well as philosophers. aXerxes bDarius I cPericles dCyrusRAINLIEST Betty Friedan was aleader in theWomen's RightsMovement byfighting what 7. Below are the steps taken to simplify the expression. Which justification matches Step c of the simplified expression? * 7x+8y+5x+3(y+1)a. 7x + 8y + 5x + 3y + 3b. 7x + 5x + 8y + 3y + 3 c. (7x + 5x) + (8y + 3y) + 3 d. 12x + 11y+ 3 A. Associative Property of AdditionB. Commutative Property of Addition C. Combine Like Terms D. Distributive Property Which of these do NOT show malleability a) Iron b) Sulfur c) Copper d) Aluminum I need some help. Can someone assist me with this? suppose the income tax rate is 4% determine the amount of money remaining after paying income tax on an income of $20,000 why did the gradute students and professors score lower than chimpanzees in Rosling's global health pre test? Oliver lives in a state with no state income tax. He pays $180 in payroll tax each week. If the federal income tax is 0.75 of the payroll tax, how much are the other taxes? -4--7=n cual es el valor de n