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NARA [144]
2 years ago
7

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.
Mathematics
1 answer:
Tresset [83]2 years ago
8 0

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 \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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 \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

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 \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

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

This means that p = \frac{99}{99+78} = 0.5593

Mean and standard deviation:

\mu = p = 0.5593

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

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

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{0.61 - 0.5593}{0.0373}

Z = 1.36

Z = 1.36 has a pvalue of 0.9131

1 - 0.9131 = 0.0869

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

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I need help with this work
Anton [14]

Answer:

Please find the answer in the image attached

Step-by-step explanation:

Here we are asked to solve a pair of linear inequalities.

In order to do so , we are first required to plot the two lines with inequalities taking into considerations.

Hence let us plot

x+2y=-4 and 5x+2y=4

let us first plot x+2y=-4

y=\frac{-4-x}{2}

let us plot a table for the same for two random values of x and putting them into above equation

x     y

0    -2

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Let us now plot these points and join the line .

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Which is not true , Hence we shade the portion divided by our line which does not contain (0,0)

Now let us plot the second line 5x+2y=4

y = \frac{4-5x}{2}

let us plot a table for the same for two random values of x and putting them into above equation

x     y

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Please refer to the image attached with this answer.

now the commonly shaded area as shown in the image will be our solution to the above pair of in equations.

3 0
3 years ago
A store buys a jacket for $20.00 and sells it to customers for 80% more than that. What is the selling price of the jacket
Tamiku [17]
38 because 80% of 20 is 18 and then add the 2
5 0
2 years ago
Please Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Katyanochek1 [597]
X - 5
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That is the answer hope this helps !
3 0
2 years ago
Solve the equation and check the solution 7/80=-1/8g​
algol13

Answer:

Exact Form: g= -7/10

Decimal Form: g= -0.7

Step-by-step explanation:

Hope this helped

7 0
3 years ago
for a certain manufacturer, only 4/5 of the items produced are not defective. if 2000 items are manufactured in a month how many
Alborosie
You need to multiply 4/5*2,000/1.

So, you would get 8,000/5.

Now, we need to divide 8,000 by 5, which would be 1,600.

1,600 items produced out of 2,000 are not defective.
5 0
3 years ago
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