1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
NARA [144]
3 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]3 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.

You might be interested in
You volunteer to help drive children at a charity event to the​ zoo, but you can fit only 7 of the 20 children present in your v
mina [271]

Answer:

for of the vans will have 0.5 and ond will have 0.3

Step-by-step explanation:

7 0
3 years ago
Dustin collects football cards.
Setler79 [48]
<em>Total Price = 3+5+5+8+8+10+10+10+40 = 99

</em>
\frac{99}{9} =11<em>
</em>
6 0
3 years ago
-3-6x=9 please help solve for x!!!!
Vinil7 [7]

Answer: x= -2

Step-by-step explanation:

Here you go!

7 0
3 years ago
0.000000205<br> In standard form
zalisa [80]

Answer:

2.05 × 10⁷

Step-by-step explanation:

0.000000205

We'll move the decimal point after the first non-zero digit (as per the scientific notation rules) and the standard form would be :

=> 2.05 × 10⁷

6 0
3 years ago
Read 2 more answers
Expand and simplify these 6 questions
zhuklara [117]
First one: divide multiply 2(1x) which would equal 2x then do 2*3 then u would subtract 5 which should get you to the simplified form 2x+1

Second one: do 3(1x) which would equal 3x then do 7*3 which would equal 21 than do plus 3x which should get you to the simplified form of 6x+21

Third one: Do 4(1x) which equals 4x than do 4*2 which equals 8 than plus eight which should get you to the simplest form of 4x+16

Fourth one: do 4(1x) which would equal 4x then do 4*1 which equals 4 than subtract 6 which should get you to the simplest form of 4x-2

Fifth one: do 2(3x) which equals 6x then do 2*2 which equals 4 than subtract 5x which should get you to the simplest form of x+4

Sixth one: do 5(1x) which equals 5x than do 5*-4 which equals -20 than add 10 which gets you to the simplest form of 5x-10
3 0
3 years ago
Other questions:
  • Will the square roots of perfect squares always be irrational numbers
    7·2 answers
  • How do you do domain and range​
    10·1 answer
  • How does a bar diagram help you understand what it means to divide fractions?
    9·1 answer
  • Chad casts a shadow that is 14.3 feet long. The straight-line distance from the top of Chad’s head to the end of the shadow crea
    14·1 answer
  • A truck has 4 crates of apples each crate has an equal number of apples all together the truck is carrying 1728 apples how many
    15·1 answer
  • How do u guys solve this?
    15·1 answer
  • I need help on this problem please
    5·2 answers
  • Kurt runs diagonally across a rectangular feild u get the resr just read the image
    11·1 answer
  • 14. The measure of Fis 110. The measure of 2E is 100°<br> What is the measure of D?<br> 150°
    10·1 answer
  • One number is 11 less than the other number if their sum is increased by 8 the results is 71
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!