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

the difference of 17 and 5 times a number (s)​

Answers

Answer:

(17-5)x

Step-by-step explanation:

the x next to the parenthesis means multiplication

Answer:

17 - 5s

Step-by-step explanation:

difference = minus sign

5 times = 5s

i feel like i have the answer, i’m just not sure and need someone else to help me so i can check it.

Answers

Answer:

5

Step-by-step explanation:

2/6=x/15

cross multiply

6x=30

x=5

What is the measure of the third angle in the yellow​ triangle?

Answers

Answer:

54

Step-by-step explanation:

66+60=126

180-126=54

A newsletter publisher believes that 49% of their readers own a personal computer. A testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. After performing a test at the 0.05 level of significance, the testing firm decides to reject the null hypothesis. What is the conclusion regarding the publisher's claim?

Answers

Answer:

The conclusion regarding the publisher's claim is that the 49% of their readers  own a personal computer.

Step-by-step explanation:

The null hypothesis is always opposite of the claim . If the null hypothesis is rejected it means the claim is accepted.

The alternate hypothesis ( claim) is

Ha: u = 0.49

The null hypothesis  is

H0 : u ≠ 0.49

The null hypothesis is rejected. The claim is accepted.

The claim ( alternate hypothesis ) was the newsletter publisher believe which is accepted.

The conclusion is drawn that the newsletter publisher was accurate that 49% of their readers  own a personal computer.

The coordinates of three vertices of a rectangle are (-4, 1), (-1, 3), and (-4, 3). Which of these points is the fourth vertex?

Answers

Answer:

The answer is (-1, 1)

Please help for 10 ponits

Answers

Answer:

it's a yes

Step-by-step explanation:

X/6 ≤ 30

to find the value of X we have to move the numerical to the other side

in this case the number is 1/6

X * 1/6 ≤ 30

so to balance the both side and get rid of the number on the left side we multiple with 6.

1/6*6 = 1 on the left side

30*6 = 180 on the right side

so the full equation will be

X * 1/6 * 6 ≤ 30 * 6

X * 1 ≤ 180

X ≤ 180

If two lines are skew lines, then they are not parallel

Answers

Answer:

Hello~

Llamalover here!

Skew lines are never parallel.

Skew lines are non-coplanar lines that do not intersect,

and parallel lines are coplanar lines that do intersect.

Step-by-step explanation:

I hope this helps!

Brainly?

In 3D geometry, diagonal lines are two lines that do not intersect and are not parallel. A simple example of a pair of diagonal lines is a pair of lines that pass through the opposite edge of a regular tetrahedron.

Can diagonal lines be parallel?

Some pairs of diagonal lines are also parallel. This is incorrect. By definition, diagonal lines are on different planes and parallel lines are on the same plane. The two lines can be diagonal or parallel (or both), but not both.

The position of the twist is two lines that do not intersect and are not parallel to each other. Diagonal lines can only exist in dimensions higher than 2D space. They do not have to be coplanar. That is, such lines are in different planes. In a two-dimensional space, two straight lines can intersect or run parallel to each other.

Learn more about skew lines here: https://brainly.com/question/2099645

#SPJ2

One box holds six eggs. If the farmer has 594 eggs, how many boxes of eggs does he have ​

Answers

Divide total eggs by number of eggs per box:

594 / 6 = 99

They has 99 boxes of eggs.

Answer:

594÷6=99

Step-by-step explanation:

YOU DIVIDE THE SUM OF EGGS AND THE NUMBER OF BOX HOLDING

A manager at a local manufacturing company has been monitoring the output of one of the machines used to manufacture chromium shells. Past data indicate that if the machine is functioning properly, the length of the shells produced by this machine can be modeled as being normally distributed with a mean of 118 centimeters and a standard deviation of 8 centimeters. Suppose 16 shells produced by this machine are randomly selected. What is the probability that the average length of these 16 shells will be between 116 and 120 centimeters when the machine is operating "properly?" Please type your answer in 3 decimal places.

Answers

Answer:

0.682 = 68.2% probability that the average length of these 16 shells will be between 116 and 120 centimeters when the machine is operating "properly".

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.

Normally distributed with a mean of 118 centimeters and a standard deviation of 8 centimeters.

This means that [tex]\mu = 118, \sigma = 8[/tex]

Sample of 16 shells

This means that [tex]n = 16, s = \frac{8}{\sqrt{16}} = 2[/tex]

What is the probability that the average length of these 16 shells will be between 116 and 120 centimeters when the machine is operating "properly?"

This is the pvalue of Z when X = 120 subtracted by the pvalue of Z when X = 116.

X = 120

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

By the Central Limit Theorem

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

[tex]Z = \frac{120 - 118}{2}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.841

X = 116

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

[tex]Z = \frac{116 - 118}{2}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.159

0.841 - 0.159 = 0.682

0.682 = 68.2% probability that the average length of these 16 shells will be between 116 and 120 centimeters when the machine is operating "properly".

PLEASE HELP
A family originally bought a home for $712,980. Now, a few years later, the home is
worth $1,180,627.70. What was the percent of increase in its value? (Round your answer to
the nearest whole number.)

Answers

Answer:

86

Step-by-step explanation:

Find the area of the shaded polygons:

Answers

To find the area of the shaded region you must subtract the area of the circle from the area of the square. , where is the side of the square and is the radius of the circle.

Answer:

4 sq. un

Step-by-step explanation:

Simplify the following expression
7-5/6.7-7/6

Answers

Simplify the following expression 7-5/6.7-7/6The answer is 1/49

22 is what percent of 40?

what is 35% of 60?

Answers

Answer:

Step-by-step explanation:

x% of 40 = 22

(x/100)×40 = 22

x = 22×100/40 = 55

22 is 55% of 40

:::::

35% of 60 = 0.35×60 = 21

Answer:

[tex]\huge\boxed{55\%}\\\boxed{21}[/tex]

Step-by-step explanation:

22 is what percent of 40?

[tex]\dfrac{22}{40\!\!\!\!\diagup}\cdot100\!\!\!\!\diagup\%=\dfrac{22\cdot10}{4}\%=\dfrac{11\cdot5}{1}\%=55\%[/tex]

[tex]p\%=\dfrac{p}{100}\\\\35\%=\dfrac{35}{100}=0.35\\\\35\%\ of\ 60\to \dfrac{35}{100\!\!\!\!\diagup}\cdot60\!\!\!\!\diagup=\dfrac{35\cdot6}{10}=\dfrac{210}{10}=21[/tex]

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

7/15

Step-by-step explanation:

Multiples of 3 = 3, 6, 9, 12, 15

Multiples of 5 = 5, 10, 15

3, 5, 6, 9, 10, 12, 15 = 7 numbers

Probability = 7/15

Hope that helps!

Answer:

7/15

Step-by-step explanation:

Because it is the "Correct Answer"

How many solutions does the system of equations have?
Choose the correct response.
O A One. The lines intersect at only one point.
O B. Infinitely many. The lines are the same.
O C Infinitely many. The lines are parallel.
D. None. The lines are parallel.

Answers

it is D :) hope this helps!

How to add angle pairs? Pls help

Answers

Complementary angle pairs add to 90

PLZ HELP ME OUTTTTTTTTT
66 points

Answers

Answer:

The vertex is at [tex](0, -9)[/tex]

The axis of symmetry [tex]x = 0[/tex]

Step-by-step explanation:

Note: You can answer all the questions looking at the graph

We have the function [tex]f: \mathbb{R} \rightarrow\mathbb{R}[/tex](I am assuming this) such that [tex]f(x) = y = (x-3)(x+3)[/tex]

We note that

[tex](x-3)(x+3) = x^2-9[/tex] once we have a difference of squares

Therefore, we have a quadratic function.

So

[tex]y = x^2-9[/tex]

The vertex [tex](h, k)[/tex] is

[tex]h = \dfrac{-b}{2a} = \dfrac{-0}{2 \cdot 1} = 0[/tex]

[tex]k= h^2 - 9 = 0^2 - 9 =-9[/tex]

Therefore, the vertex is at [tex](0, -9)[/tex]

As we know the vertex, we conclude that the axis of symmetry [tex]x = 0[/tex]

The x-intercepts occur at [tex]y = 0[/tex]

[tex]y = (x-3)(x+3) \implies x = -3, x=3[/tex]

So, the left x-intercept is [tex](-3, 0)[/tex] and the right x-intercept is [tex](3, 0)[/tex]

As I stated in the beginning, the domain is the set of all real numbers. Precisely,

[tex]Dom(f) = \mathbb{R} = (-\infty, \infty)[/tex]  

Once, we know the vertex, we also conclude that the Range is

[tex]Ran(f)= [-9,\infty)[/tex]

Greater than or equal to -9

Robin hood plans to use a 54 ft ladder to reach the castle window of Maid Marian. Little John, who made the ladder, advised Robin that the angle of elevation of the ladder must be between \displaystyle 55^{of}55 o and \displaystyle 70^{of}70 o for safety. What are the minimum and maximum heights that can safely by reached by the top of the ladder when it is placed against the 50 ft castle wall

Answers

Answer:

The minimum height is: 44.24 ft and the maximum is 50.74ft

Step-by-step explanation:

Given

[tex]L = 54[/tex] --- Length of ladder

[tex]55 \le \theta \le 70[/tex]

Required

The minimum and maximum height

The question is illustrated with the attached image:

The height h is calculated using:

[tex]\sin(\theta) = \frac{h}{54}[/tex] --- sine equation

When [tex]\theta = 55[/tex], we have:

[tex]\sin(55) = \frac{h}{54}[/tex]

Make h the subject

[tex]h = 54 * \sin(55)[/tex]

[tex]h = 54 * 0.8192[/tex]

[tex]h = 44.24ft[/tex]

When [tex]\theta = 70[/tex], we have

This gives:

[tex]\sin(70) = \frac{h}{54}[/tex]

Make h the subject

[tex]h = 54 * \sin(70)[/tex]

[tex]h = 54 * 0.9397[/tex]

[tex]h = 50.74ft[/tex]

The minimum height is: 44.24 ft and the maximum is 50.74ft

Determine the length of DE.

Answers

It is 5 ! :) because since the triangle ABC = DEF The measurements will be the same. The formula for finding the DC (hypothenuse) is a squared + b squared = c squared


Plug it in-
3*3=9
4*4=16
9 + 16 =25
Find the square root of 25 which brings the answer to 5 :)

You have 12 gallons of punch. You estimate that each guest will drink 3 cups. Do you have enough punch for 60 guests?

Answers

Answer:i got 1 2 3 4 5 6 7 8 shooters ready to gun you down

Step-by-step explanation:

what is the value of x ?
a. 10.4
b. 52
c. 61.6
d. 92

Answers

the answer is 10.4 because 180 - 128 is 52 then divide by 5 which gives you 10.4 :)

help asap please!!!!

Answers

Answer:

F=(-1, -2)

G=(-3, -5)

H=(-3, -2)

Step-by-step explanation:

PLS HELP

Cindy wants to sell 300 shares of a company’s stock at the market price of $25 per share. She looks up online brokers and the fees they charge. Arrange the brokers’ fees in order from least to greatest.


(i looked at other brainly answers to this question and they were all different to each other like there were 3 diff answers)

Answers

Answer:

Step-by-step explanation:

It's in the same order, from broker 1 down to broker 5. Straight up

Answer:
Broker E
|
V

Broker C
|
V

Broker D
|
V

Broker B
|
V

Broker A

PLS HELP AND ANSWER QUICK PLZ

Answers

Answer:

X = 90° , Y = 45°,  Z = 45°

Step-by-step explanation:

PLS ANSWER ASAP THANKS

Answers

x = 95°

The angles are vertically opposite so they are equal.

One day, a restaurant chef reports that 28% of the meals served included chicken. What fraction of the meals served that day included chicken? Write the fraction in simplest form.

Answers

Answer:

72%

Step-by-step explanation:

72%+28=100%

Another submarine's descent can be represented as y=-240x, where y is the elevation and x is the time in hours. How long did it take the submarine to descend to the seafloor 2,100 feet below the surface?

Answers

Answer:

8 hours and 45 minutes

Step-by-step explanation:

-2100 divided by -240 = 8.75 or 8 hours and 45 minutes

what is the AREA of the buildings in Volume city?​

Answers

Where is volume city?

What is the average rate of change of g over the interval [-1 4]

Answers

Answer:

your answer will be -1.2

Step-by-step explanation:

hope it helps you

have a great day

Right triangle ABC has hypotenuse AB = 12 and acute angle A = 75°. Find
Leg CB

Answers

Answer:

Leg CB = 11.59 unit (Approx.)

Step-by-step explanation:

Given:

ABC is a right triangle

Hypotenuse AB = 12

Acute angle A = 75°

Find:

Leg CB

Computation:

Using trigonometry function;

Sin θ = Perpendicular / Hypotenuse

Sin 75 = Perpendicular / 12

0.9659 = CB / 12

Leg CB = 11.59 unit (Approx.)

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