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.
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?
what is the total surface area in square millimeters, of the rectangle solid shown below? HELP PLEASE!
Answer:
D) 290
Step-by-step explanation:
w = 5
l = 12
h = 5
Formula:
SA = 2(wl + hl + hw)
SA = 2(5*12 + 12*5 + 5*5)
SA = 2(60 + 60 + 25)
SA = 2(145)
SA = 290
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:
Simplify -3 p3 + 5 p + (-2 p2 ) + (-4) - 12 p + 5 - (-8 p3 ). Select the answer in descending powers of p . 1 - 7 p - 2 p2 + 5 p3 1 + 7 p + 2 p2 - 5 p3 5 p3 - 2 p2 - 7 p + 1 -5 p3 + 2 p2 + 7 p + 1
Step-by-step explanation:
Let's simplify step-by-step.
−3p3+5p−2p2−4−12p+5−−8p3
=−3p3+5p+−2p2+−4+−12p+5+8p3
Combine Like Terms:
=−3p3+5p+−2p2+−4+−12p+5+8p3
=(−3p3+8p3)+(−2p2)+(5p+−12p)+(−4+5)
=5p3+−2p2+−7p+1
Answer:
=5p3−2p2−7p+1
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
The functions q and r are defined as follows.
q(x)+−5x5
r(x)+−2x5
Find the value of r(q(−1)).
Answer:
eat
Step-by-step explanation:
eat
The table shows the amount in fluid ounces of
each ingredient Randolph used to make fruit
punch for a party.
How many pints of this fruit punch did Randolph
make?
Fruit Punch
1,792 pints
Ingredient
Amount Used
(fluid ounces)
B 102 pints
Orange juice
24
7 pints
Apple juice
24
Lime soda
64
D 14 pints
Answer:
Step-by-step explanation:
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
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.
Find the zeros of the function. Enter the solutions from least to greatest . h(x) = (- 4x - 3)(x - 3) lesser x = greater
9514 1404 393
Answer:
-3/4, 3
Step-by-step explanation:
The zeros are the values of x that make h(x)=0. Those are the values of x that make the factors of h(x) be zero.
-4x -3 = 0 ⇒ x = -3/4
x -3 = 0 ⇒ x = 3
The zeros of the function are -3/4 and 3.
Plssss helppppppl:((((
Answer:
I think it's 1.5 I'm not sure ._.
Answer:
1/3
Step-by-step explanation:
Total students = 36
No of boys = 24
No of girls = 36 - 24 = 12
Probability of selecting a girl = 12/36 = 1/3
you are given the quadratic function: f(x) = 3x{2} + 4x - 2 Find the value of f(-1)
will mark brainliest!!! PLEASSE HELP! show work too
Answer:
f(-1) = -3
Step-by-step explanation:
(Assuming {2} is ^2)
f(-1) = 3(-1)² + 4(-1) - 2
= 3(1) - 4 - 2 = -3
PLEASE HELP!!
The scale on a map reads 0.5 inch = 30 miles. If two cities on the map are 5.75 inches apart, find the actual distance
between the cities.
Answer:
345 miles
Step-by-step explanation:
So we know that 2 cities are 5.75 inches apart on the map and the scale reads for every 0.5 inch its 30 miles. So we can first start of by diving 5.75 by 0.5, since we need to know how many “0.5” inches are in 5.75 inches. You’d get 11.5. Now 11.5 multiply that by 30 which would get you 345 miles.
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
Match each equation with its graph. y = 5x + 2, y = 3x + 3, y = 2x + 3
Answer:
Green line: y = 5x + 2
Red line: y = 3x + 3
Purple line: y = 2x + 3
Step-by-step explanation:
1) All the given equations are in slope-intercept form, or [tex]y = mx + b[/tex] format. When an equation is written in this form, the constant on the right side of the equation, or the [tex]b[/tex], represents the y-intercept. The y-intercept is the point at which the line crosses the y-axis.
Knowing this, the y-intercept of [tex]y = 5x + 2[/tex] must be (0,2). The only graph in which the line crosses the y-axis at the point (0,2) is the one with the green line, thus the graph of [tex]y = 5x + 2[/tex] is the green one.
2) Now, since the other two equations share the same y-intercept, we have two graphs left. We can find out which graph belongs to which equation by taking a look at the slope of the line. The number in place of [tex]m[/tex], or the coefficient of the x-term in an equation in slope-intercept format represents the slope. Thus, the slope of [tex]y = 3x +3[/tex] is 3 and the slope of [tex]y = 2x + 3[/tex] is 2.
Now, find the slope of one of the lines in the graphs. To do so, use the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute the x and y values of two points on the chosen line into the formula in order to figure out the line's slope. I chose to find the slope of the red line, using the points (0,3) and (-1,0):
[tex]m = \frac{(0)-(3)}{(-1)-(0)} \\m = \frac{0-3}{-1-0}\\m = \frac{-3}{-1} \\m = 3[/tex]
So, the slope of the red line is 3. Its equation must be [tex]y = 3x + 3[/tex] since it has the matching slope. By process of elimination, the purple line must have the equation of [tex]y = 2x + 3[/tex].
The Matching is:
Green line: y = 5x + 2Red line: y = 3x + 3Purple line: y = 2x + 3What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
We know the slope- intercept form
y= mx+ b
where m is the slope.
For y= 5x+ 2 the slope is 5.
and, for y= 3x+ 3 the slope is 3.
and, for y= 2x+ 3 the slope is 2.
For Graph 1, the slope is 5/1= 5
and, For Graph 2, the slope is 6/2= 3
and, For Graph 3, the slope is 6/3 = 2
Learn more about slope here:
https://brainly.com/question/3605446
#SPJ2
A farmer's market sells Apple's for $2.30 per pound what would be the cost of 3\2\5
Answer:
3 lb = $6.90
2 lb = $4.30
5 lb = $11.50
Step-by-step explanation:
Answer:
The cost of 3 apples: $6.90
The cost of 2 apples: $4.60
The cost of 1 apple: $2.30
Step-by-step explanation:
2.30 times 3 equals $6.90
2.30 times 2 equals $4.60
2.30 times 1 equals $2.30
Side Note:
hope this helps have a nice day :)
Write an equation that represents each side of the figure. Write your equations in slope-intercept form.
Answer:
Top: y=3
Top right: y=-3/2x+6
Bottom right: y=3/2x-6
Bottom: y=-3x
Bottom left: y=-3/2x-6
Top left: y=3/2x+6
Step-by-step explanation:
Top: y=3
Top right: y=-3/2x+6
Bottom right: y=3/2x-6
Bottom: y=-3x
Bottom left: y=-3/2x-6
Top left: y=3/2x+6
Should my answer be 85=360+12h
Answer:
h = [tex]\frac{- 275}{12}[/tex]
Step-by-step explanation:
85 = 360 + 12h
85 - 360 = 360 - 360 + 12h
- 275 = 12h
- 275 ÷ 12 = 12h ÷ 12
h = - 275/12
A research firm conducted a study to determine the average amount of money that smokers spend on cigarettes during a week. The firm found that the population mean amount that all smokers spend on cigarettes is $20 and the population standard deviation is $5. What is the probability that a new sample this year of 100 steady smokers spends between $19 and $21 on average
Answer:
0.9544 = 95.44% probability that a new sample this year of 100 steady smokers spends between $19 and $21 on average
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 zscore 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 pvalue, 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.
The firm found that the population mean amount that all smokers spend on cigarettes is $20 and the population standard deviation is $5.
This means that [tex]\mu = 20, \sigma = 5[/tex]
Sample of 100:
This means that [tex]n = 100, s = \frac{5}{\sqrt{100}} = 0.5[/tex]
What is the probability that a new sample this year of 100 steady smokers spends between $19 and $21 on average?
This is the pvalue of Z when X = 21 subtracted by the pvalue of Z when X = 19. So
X = 21
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{21 - 20}{0.5}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 19
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{19 - 20}{0.5}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.9772 - 0.0228 = 0.9544
0.9544 = 95.44% probability that a new sample this year of 100 steady smokers spends between $19 and $21 on average
Which graph represents a function?
Answer:
C
Step-by-step explanation:
In D, the x value repeats
Answer:
C
Step-by-step explanation:
C has a positive then negative slope, while D can't even be a function.
I hope this helps :)
Describe how the graph of y=2x and y=2x+7 are the same.
Answer:
These two equations produce a similar graph because they both share the same slope: 2. The only difference is that the y-intercept for the second equation is a positive 7, making the graph shift upwards. Other than this, both equations would be parallel (and identical) on the graph.
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 arithmetic mean of 64 and 69
Answer:
66.5
Step-by-step explanation:
64+69=133
133÷2=66.5
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.
Which equation represents the line shown on the coordinates grid below?
the height, in feet, of Ferris wheel rider t seconds after the ride begins is given by h(t)=-35cos(2t)+45. What is the average rate of change of height, in feet per second, from time t=30 to t=45? (radians)
Answer: b
Step-by-step explanation: the answer is got was 1.166666
A band director is trying to decide what music to play for the halftime show. She surveys the marching band
students to get their opinions about which music they would prefer. Which of the following sampling techniques
would provide a stratified random sample that would accurately represent the students' opinions?
Have a computer randomly sort the band members, then select the first 30.
O Randomly select 2 students from each type of instrument (trumpet, saxophone, clarinet, etc.).
O Randomly pick a letter of the alphabet and survey every student whose last name begins with that letter.
Randomly pick a year of students (freshman, sophomore, junior, or senior) and survey every student from the
selected group
Mark this and retum
Save and Exit
Nex
Submit
Answer:
B
Step-by-step explanation:
A new centrifugal pump is being considered for an application involving the pumping of ammonia. The specification is that the flow rate be more than 3 gallons per minute (gpm). In an initial study, eight runs were made. The average flow rate was 6.3 gpm and the standard deviation was 1.9 gpm. If the mean flow rate is found to meet the specification, the pump will be put into service.
a) State the appropriate null and alternate hypotheses.
b) Find the P-value.
c) Should the pump be put into service? Explain.
cuál es la regla algebraica ? por favor
Answer:
esto es correcto, la y sigue siendo la misma
Step-by-step explanation:
Answer: y=4
Step-by-step explanation:
y = 4
Por que y siempre es equitativo a cuatro.
Perdón por los errores en mi español. Es mi segundo idioma.