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.
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.
What is 5x20
Me will give a brainliest for this easy question so hurry up
Answer:
100
Step-by-step explanation:
20+20+20+20+20=100
Hope this helps
Please give me brailiest
A rectangular piece of land is 1/4 mile long and a 1/2 mile wide. What is the area of this piece of land in square miles?
Lewis directs the school marching band. He uses scale drawings of the football field to design marching formations for the band. The football
field is 100 yards long and 53 yards wide. Lewis always uses a scale of 1 inch to 10 yards for his drawings.
Complete the steps below to find the length and width of the football field as it appears in one of Lewis's scale drawings.
Aa
Part A
What is the actual area of the football field? Assume that the field is shaped like a rectangle.
Answer:
Actual area of the field = l×b
=100×531/3 sq. yards
=100×177 sq. yards
= 17700 sq. yards
Step-by-step explanation:
pls mark brainliest
Please answer this correctly without making mistakes I want ace expert and genius people to answer this correctly without making mistakes
Answer:
2q-10
Step-by-step explanation:
The product of 2 and q is 2q and ten fewer than that 2q-10
You randomly survey men and women about whether they plan to watch a new television show on Sunday afternoon. A total of 15 men
plan to watch the new show and a total of 12 women do not plan to watch the new show. A total of 40 women are surveyed. A total of
42 people do not plan to watch the new television show. How many people did you survey?
Answer:
.
Step-by-step explanation:
Identify each pair of angles as corresponding, Alternate interior, alternate exterior, or consecutive interior and solve for X
Answer:
Step-by-step explanation:
19). Angles measuring 90° and (21x + 6)° are Alternate exterior angles.
Therefore, 21x + 6 = 90
2x = 90 - 6
2x = 84
x = 42
21). Angles measuring 60° and (8x - 4)° are Alternate interior angles,
8x - 4 = 60
8x = 60 + 4
x = [tex]\frac{64}{8}[/tex]
x = 8
23). Since, angles measuring (-1 + 14x)° and (12x + 17)° are Alternate exterior angles
Therefore, (-1 + 14x) = (12x + 17)
14x - 12x = 17 + 1
2x = 18
x = 9
25). Both the angles (x + 96)° and (x + 96)° are consecutive interior angles.
Therefore, (x + 96)° + (x + 96)° = 180° [Property of consecutive interior angles]
2x + 192 = 180
2x = 180 - 192
2x = -12
x = -6
Now measure of (x + 96)° = -6 + 96
= 90°
26). Both the angles (20x + 5)° and (24x - 1)° are consecutive interior angles.
Therefore, (20x + 5)° + (24x - 1)° = 180°
44x + 4 = 180
44x = 176
x = 4
the store employee works 35 hours per week,which inequality can be used to find the dollar value x, of weekly sales that the employee must make to earn more than $400 per week
A.) 35(8)+0.08x<400
B.) 35(8)+0.08X>400
C.) 35(0.08)+8X<400
D.) 35(0.08)+8X>400
pls help find the answer !!
FIND EG
Answer:
EG = 7
Step-by-step explanation:
The parallel lines cut sides AB and AC into segments with proportional lengths.
AB/DF = AC/EG
(AD + DF + FB)/DF = AC/EG
(18 + 10 + 12)/10 = 28/EG
40/10 = 28/EG
4 = 28/EG
4EG = 28
EG = 28/4
EG = 7
Hunter correctly answered 79% of questions on his last science test. If he
answered 30 questions correctly, how many questions were on the test?
Round your answer to the nearest whole.
Answer:
37
Step-by-step explanation:
If 30 questions is 79% of the test, then you would need to divide 30/0.79(79%), which equals 37 questions in total on the test.
The ratio of the angles of a triangle is 3:7:2. What is the measure of the largest angle?
Answer:
the largest angle is 150°
a local hamburger shop sold a combined total of 613 hamburgers and cheeseburger on Friday. there were 63 more cheeseburger sold than hamburger. How many hamburger were sold on friday
Answer:
275 hamburgers was sold on Friday
Find the measure of an angle that is positive and less than 360° in standard position for each reference angle.
9514 1404 393
Answer:
112°285°202°Step-by-step explanation:
In quadrant II, the standard position angle is found by subtracting the reference angle from 180°.
180° -68° = 112°
__
In quadrant IV, the standard position angle is found by subtracting the reference angle from 360°.
360° -75° = 285°
__
In quadrant III, the standard position angle is found by adding 180° to the reference angle.
180° +22° = 202°
Rewrite without absolute value for the given conditions: y=|x-3|+|x+2|-|x-5|, if 3 If you put a link i will not hesitate to report you
Answer:
Don't know if this is right but it should maybe be y= x+3+x+2-x+5 because You cant have a negative in absolute values.
Help pleaseee!!!!!!!!!!!!!!!!!!
Answer: 6.6667% or 2/30
The distance from the pitcher’s mound to home plate is 60.5 feet. Does this form a right triangle with first base? Explain your reasoning
Answer:
NO.
Step-by-step explanation:
60.5 + 60.5 = 121
find the sum of the odd numbers between 100 and 200
Answer:
50
Step-by-step explanation:
there are 100 numbers between 100 and 200
50 that are even 50 that are odd
Answer:
137 + 63 = 200
Step-by-step explanation:
I need help with c please.
Answer:
||w|| = 6
Step-by-step explanation:
||w|| = modulus or magnitude of vector w
Since formula to get the modulus of any vector = [tex]\sqrt{\text{(x-component)}^2+\text{(y-component)}^2}[/tex]
Vector w = <-6, 0>
x-component of vector w = (-6)
y-component of vector w = 0
Therefore, ||w|| = [tex]\sqrt{(-6)^2)+(0)^2}[/tex]
= 6
Answer It, Thanks. -3(-100)
Answer: 300
Step-by-step explanation:
Answer:
300
Step-by-step explanation:
If all terms are negative then the result will come out positive.
What is 39.79949748 rounded to the nearest hundredth?
Answer:
[tex]Number = 39.80[/tex]
Step-by-step explanation:
Given
[tex]Number = 39.79949748[/tex]
Required
Approximate (to the nearest 100th)
This means that, we approximate at the second digit after the decimal.
So:
i.e,
Number = 39.79 [Begin approximation] 949748
The first digit after [Begin approximation] is then approximated using the following rule:
[tex]0 - 4 \approx 0[/tex]
[tex]5 - 9 \approx 1\\[/tex]
Since 9 falls in [tex]5 - 9 \approx 1\\[/tex] category, the number becomes:
[tex]Number = 39.[79+1][/tex]
[tex]Number = 39.80[/tex]
In ΔKLM, k = 4.4 cm, l = 3.1 cm and ∠M=150°. Find the length of m, to the nearest 10th of a centimeter.
The value of length m is 2.13cm
What is cosine rule?In trigonometry, the Cosine Rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
therefore m² = k²+l²+2klCos M
m² = 4.4²+3.1²+ 2× 3.1×4.4cos 150
m² = 19.36+9.61+27.28(-0.8660)
m² = 28.97-23.62
m² = 5.35
m = √5.35
m = 2.31 cm( nearest tenth)
Therefore the measure of length m is 2.31 cm
learn more about cosine rule from
https://brainly.com/question/23720007
#SPJ1
help with math will give u 5 star if right!!!
Answer:
Its b
Step-by-step explanation:
just add it all together :)
Hope this helps :)
Answer:
The 2nd statement
i need help with this 1 question
7 × 8 × 8 = 448
and that's it
Which fraction is equivalent to
3/5
Answer:
12/20
Step-by-step explanation:
One-fourth of the flower bulbs need to be planted before dark. If there are 6 people to do the
planting and each person plants the same number of bulbs, what fraction of the total number
of bulbs does each person plant?
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
What is the value of y?
Answer:
95°
Step-by-step explanation:
120° = 25° + y ( exterior angle of a triangle is equal to the sum of two opposite interior angles)
y = 120° - 25°
y = 95°
Hope it will help :)❤
what are 3 ratios equivalent to 4/6 ?
Answer:
Answer is 400:600,6:9,66:99
Step-by-step explanation:
I hope it's helpful!
Answer:
8:12, 16:24 , 32:48
Step-by-step explanation:
'
!
(X+3)(x+4) factor the trinomial
Answer:
[tex]x^{2} + 7x + 12[/tex]
Step-by-step explanation:
This is already factored so I assume you meant expand it.
Where would it go I know how to do X axis but not Y
Answer: (-1,2) and (2,2) Make sure to see explanation!
Step-by-step explanation:
Well you need to remember the Y reflection rule!
To reflect over the Y axis you must do this:
Take the points in this case
(1,2) and (-2,2)
And you need to use the equation (x,y) --> (-x,y)
So the new points you NEED TO GRAPH ARE
(-1,2) and (2,2)
Hope this helped!
Answer: (-1,2) and (2,2)
Step-by-step explanation:
reflection over the y axis, take the point (x,y) and change the sign of the X-value (-x,y). When You reflect over the y-axis, the y remains the same.
point (1,2) would become (-1,2) reflected over the Y
and (-2,2) would become (2,2)
I need help please help