Answer:
The correct answer to the following question will be "No". The further explanation is given below.
Step-by-step explanation:
Probability (Keeping the disease out of 1 contact)
= [tex]0.5[/tex]
Probability (not keeping the disease out of 1 contact)
= [tex]1-0.5[/tex]
= [tex]0.5[/tex]
Now,
Probability (not keeping the disease out of 2 contact)
= Keeping the disease out of 1 contact × not keeping the disease out of 1 contact
On putting the estimated values, we get
= [tex]0.5\times 0.5[/tex]
= [tex]0.25[/tex]
So that,
Probability (Keeping the disease out of 2 contact)
= [tex]1-0.25[/tex]
= [tex]0.75 \ i.e., 75 \ percent[/tex]
∴ Not 100%
What is the value of y ??????????????
Answer & Step-by-step explanation:
For this problem we can just set up an equation and equal it to 180.
(2y) + (y + 10) + 50 = 180
Combine like terms.
3y + 60 = 180
Subtract 60 from 180.
3y = 120
Divide 120 by 3.
y = 40
So, the value of y is 40°
Which of the following is a radical equation?
X3 - 13
X+ 15 - 13
√x+3-13
x+3 - 13
Answer:
√x+3-13
Step-by-step explanation:
This answer is a radical equation because a square root is used in the equation. This makes the equation radical. The other choices have no square roots so they can't be the answers.
Let f(x)=−9x+1. Match the function with the description.
The graph of g is a reflection in the y-axis of the graph of f.
The graph of g is a reflection in the x-axis of the graph of f.
The graph of g is a horizontal translation 16 units right of the graph of f.
The graph of g is a vertical translation 16 units down of the graph of f.
Answer:
I guess that we want to find the function g(x) for the 4 cases.
first, f(x) = -9*x + 1.
a) The graph of g is a reflection in the y-axis of the graph of f.
First remember: if we have the point (x,y) and we reflect it over the y-axis, we get (-x,y)
then g(x) = f(-x) = -9*-x + 1 = 9*x + 1.
b) The graph of g is a reflection in the x-axis of the graph of f.
if we have a point (x, y) and we reflect it over the x-axis, the point transforms into (x, -y)
then we have: g(x) = -f(x) = 9*x - 1
c) The graph of g is a horizontal translation 16 units right of the graph of f.
When we want to have a translation in the x-axis, we must change x by x - A.
If A is positive, this transformation moves the graph by A units to the right, in this case, A = 16.
g(x) = f(x - 16) = -9*(x - 16) + 1
d) The graph of g is a vertical translation 16 units down of the graph of f.
For vertical translations, if we want to move the graph by A units down (A positive) we should do y = f(x) - A
In this case, A = 16.
then: g(x) = f(x) - 16 = -9*x + 1 - 16 = -9*x - 15.
Let D= {(x,y) | x^2+y^2 ≤ 4x} Using polar coordinates, What is the integral: ∬y^2/ (x^2+y^2)dxdy?
In polar coordinates, the inequality changes to
[tex]x^2+y^2\le4x\implies r^2\le4r\cos\theta\implies r\le4\cos\theta[/tex]
which is a circle of radius 2 and centered at (2, 0). The set D is then
[tex]D=\left\{(r,\theta)\mid0\le r\le4\cos\theta\land0\le\theta\le\pi\right\}[/tex]
The integral is then
[tex]\displaystyle\iint_D\frac{y^2}{x^2+y^2}\,\mathrm dx\,\mathrm dy=\int_0^\pi\int_0^{4\cos\theta}\frac{r^2\sin^2\theta}{r^2}r\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\int_0^\pi\int_0^{4\cos\theta}r\sin^2\theta\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\frac12\int_0^\pi((4\cos\theta)^2-0^2)\sin^2\theta\,\mathrm d\theta[/tex]
[tex]=\displaystyle8\int_0^\pi\cos^2\theta\sin^2\theta\,\mathrm d\theta[/tex]
There are several ways to compute the remaining integral; one would be to invoke the double-angle formula,
[tex]\sin(2\theta)=2\sin\theta\cos\theta[/tex]
so that the integral is
[tex]=\displaystyle8\int_0^\pi\frac{\sin^2(2\theta)}4\,\mathrm d\theta[/tex]
[tex]=\displaystyle2\int_0^\pi\sin^2(2\theta)\,\mathrm d\theta[/tex]
Then invoke another double-angle formula,
[tex]\sin^2\theta=\dfrac{1-\cos(2\theta)}2[/tex]
to change the integral to
[tex]=\displaystyle\int_0^\pi1-\cos(4\theta)\,\mathrm d\theta[/tex]
[tex]=(\pi-\cos(4\pi))-(0-\cos0)=\boxed{\pi}[/tex]
Round 1040 to the nearest hundred.enter your answer in the box below
Answer:
1000
Step-by-step explanation:
For rounding questions, you want to look at the place value to the right of the digit it wants you to round to. If that place value to the right of the digit you need to round is less than 5, you round down. If the place value to the right of the digit you need to round is 5 or greater, then you round up. In your situation, the place value you want to round is the hundreds place, so we need to look at the tens value. The tens value is 4, which is less than 5, so we round down. Therefore, the answer would be 1000.
2. CTfastrak bus waiting times are uniformly distributed from zero to 20 minutes. Find the probability that a randomly selected passenger will wait the following times for a CTfastrak bus. b. Between 5 and 10 minutes. c. Exactly 7.5922 minutes. d. Exactly 5 minutes. e. Between 15 and 25 minutes.
Answer:
b. 0.25
c. 0.05
d. 0.05
e. 0.25
Step-by-step explanation:
if the waiting time x follows a uniformly distribution from zero to 20, the probability that a passenger waits exactly x minutes P(x) can be calculated as:
[tex]P(x)=\frac{1}{b-a}=\frac{1}{20-0} =0.05[/tex]
Where a and b are the limits of the distribution and x is a value between a and b. Additionally the probability that a passenger waits x minutes or less P(X<x) is equal to:
[tex]P(X<x)=\frac{x-a}{b-a}=\frac{x-0}{20-0}=\frac{x}{20}[/tex]
Then, the probability that a randomly selected passenger will wait:
b. Between 5 and 10 minutes.
[tex]P(5<x<10) = P(x<10) - P(x<5)\\P(5<x<10) = \frac{10}{20} -\frac{5}{20}=0.25[/tex]
c. Exactly 7.5922 minutes
[tex]P(7.5922)=0.05[/tex]
d. Exactly 5 minutes
[tex]P(5)=0.05[/tex]
e. Between 15 and 25 minutes, taking into account that 25 is bigger than 20, the probability that a passenger will wait between 15 and 25 minutes is equal to the probability that a passenger will wait between 15 and 20 minutes. So:
[tex]P(15<x<25)=P(15<x<20) \\P(15<x<20)=P(x<20) - P(x<15)\\P(15<x<20) = \frac{20}{20} -\frac{15}{20}=0.25[/tex]
At the neighborhood block party, John noticed that every 5 minutes, the
shadow of a nearby pine tree got six inches longer. The shadow was 12
feet long at 4:15pm. How long was the shadow at 5:00pm?
Answer:
7
Step-by-step explanation:
I think because at if you divide 45 by 6 because its 45 minutes from 4:15 to 5:00 and it grows 6 inches longer every five min
This Question: 4 pts
1 of 11 (0 complete)
Music Preferences
Students at a high school were polled to determine the type of music they preferred. There were 1960 students who
completed the poll. Their responses are represented in the circle graph.
Rap 916
Alternative 46
Rock and Roll 279
Country 183
Jazz 32
Other 89
About What % of the students who completed the poll preferred rock and roll music.
(Round to one decimal place as needed.)
Answer:
The percentage of the students who completed the poll preferred rock and roll music.
P(RR) = 0.1423 = 14.23 %
Step-by-step explanation:
Explanation:-
Given total number of students n(S) = 1960
Given the Students at a high school were polled to determine the type of music they preferred.
Rap 916
Alternative 46
Rock and Roll 279
Country 183
Jazz 32
Other 89
Let ' RR' be the event of Rock and Roll preferred music
given Rock and Roll = 279
n( RR) = 279
The percentage of the students who completed the poll preferred rock and roll music.
[tex]P(RR) = \frac{n(RR)}{n(s)} = \frac{279}{1960}[/tex]
P(RR) = 0.1423 = 14.23 %
Round0.00359 to nearest ten thousand
Answer: 0.0036
Step-by-step explanation:
0.00359 — 0.0036
The nine rounds up
Can someone help me with this worksheet? Will give all my points.
Answer:
Here are the formulas
Cube/Rectangular Prism:
Volume = Length*width*height
Surface area = 2(wl+hl+hw)
Lateral area= Area of vertical faces
Base area = length*width
Regular hexagonal prism:
Volume : (3sqrt3/2)*a^2*h
Surface Area = 6ah+3sqrt(3)a^2
lateral area: 6ah
base area = 3sqrt(3)s^2/2
Triangular prism
Volume: The volume of a triangular prism can be found by multiplying the base times the height.
Surface area: A triangular prism has three rectangular sides and two triangular faces. To find the area of the rectangular sides, use the formula A = lw, where A = area, l = length, and h = height. To find the area of the triangular faces, use the formula A = 1/2bh, where A = area, b = base, and h = height.
Etc.
A charity receives 2025 contributions. Contributions are assumed to be mutually independent and identically distributed with mean 3125 and standard deviation 250. Calculate the approximate 90th percentile for the distribution of the total contributions
Answer:
The 90th percentile for the distribution of the total contributions is $6,342,525.
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 normally distributed samples are 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.
For sums of size n, the mean is [tex]\mu*n[/tex] and the standard deviation is [tex]s = \sqrt{n}*\sigma[/tex]
In this question:
[tex]n = 2025, \mu = 3125*2025 = 6328125, \sigma = \sqrt{2025}*250 = 11250[/tex]
The 90th percentile for the distribution of the total contributions
This is X when Z has a pvalue of 0.9. So it is X when Z = 1.28. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.28 = \frac{X - 6328125}{11250}[/tex]
[tex]X - 6328125 = 1.28*11250[/tex]
[tex]X = 6342525[/tex]
The 90th percentile for the distribution of the total contributions is $6,342,525.
The freezer contains vanilla and chocolate ice cream. Chocolate ice cream contains 12 servings less than vanilla. How many servings of vanilla ice cream are in the freezer if there are a total of 40 servings of ice cream? (Solve by building an equation)
Answer:
26 servings
Step-by-step explanation:
Let the number of servings of vanilla ice cream be x.
Number of servings of chocolate ice cream
= x -12
(since it has 12 servings less than vanilla)
Total servings= servings of chocolate+ vanilla
x + x-12= 40
2x -12 =40 (simplify)
2x= 40 +12 (+12 on both sides)
2x= 52 (simplify)
x= 52 ÷2
x= 26
Therefore, there are 26 servings of vanilla ice cream in the freezer.
A researcher recruited 55 adults and tested their ability to remember a list of words. For each participant, the researcher counted the number of words correctly recalled and recorded their age (in years).
HYPOTHESIS
The research hypothesis is that age is related to memory performance.
This hypothesis is:__________.
a. directional
b. non-directional
Answer:
b. non-directional
Step-by-step explanation:
A directional hypothesis can be described as a hypothesis which predicts the direction of impact, either positive or negative, of one variable, especially independent variable, on the other variable which is known as an independent variable. For example, the hypothesis "age reduces memory performance" is a directional hypothesis. The reason is that "reduces" show the direction that age has a negative effect on memory performance.
On the other hand, non-directional hypothesis can be described as a hypothesis that does not predict the direction of impact but only states the relationship between two variables. For example, the research hypothesis is in the question that "age is related to memory performance" is non-directional hypothesis. This because the word "related" in the hypothesis only indicate that there is a relationship between the two variables, not the direction of effect of one variable on the other.
(a) Use a linear approximation to estimate f(0.9) and f(1.1). f(0.9) ≈ f(1.1) ≈ (b) Are your estimates in part (a) too large or too small? Explain. The slopes of the tangent lines are negative, but the tangents are becoming steeper. So the tangent lines lie below the curve f. Thus, the estimates are too large. The slopes of the tangent lines are negative, but the tangents are becoming steeper. So the tangent lines lie below the curve f. Thus, the estimates are too small. The slopes of the tangent lines are positive, but the tangents are becoming less steep. So the tangent lines lie above the curve f. Thus, the estimates are too large. The slopes of the tangent lines are positive, but the tangents are becoming less steep. So the tangent lines lie above the curve f. Thus, the estimates are too small.
Answer:
(Missing part of the question is attached)
[tex]L(x)=2x+3[/tex]
Estimates are too large.
Step-by-step explanation:
Suppose the only information we know about the function is:
[tex]f(1)=5[/tex]
where the graph of its derivative is shown in the attachment
(a)If the function [tex]f\\[/tex] is differentiable at point [tex]x=1[/tex] , the tangent line to the graph of [tex]f[/tex] at 1 is given by the equation:
[tex]y=f(1) +f'(1)(x-1)[/tex]
So we call the linear function:
[tex]L(x)=f(1) +f'(1)(x-1)[/tex]
We know the [tex]f(1)=5[/tex] as it is given in the question, and [tex]f'(1)=2[/tex] from the graph attached. Substitute in the equation of [tex]L(x)[/tex].
[tex]L(x)=5+2(x-1)\\L(x)=5+2x-2\\L(x)=2x+3\\[/tex]
(b)At x=1, [tex]f'(x)[/tex] is positive but it is decreasing. However. if we draw the tangent lines, we see that the tangent lines are becoming less steeper, so the tangent lines lie above the curve [tex]f[/tex]. Thus, The estimates are too large.
Find the area of a circle with radius, r = 19cm.
Give your answer rounded to 3 SF.
Goods available for sale are $40000, beginning inventory is $16000, ending inventory is $20000, the cost of goods sold $50000, what is the inventory turnover
Answer:
2.78Step-by-step explanation:
Inventory turn over is the same as the inventory turn over ratio. Inventory turn over is defined simply as the ratio of the cost of goods that was sold (net sales) to the average inventory at the selling price.
Inventory turn over = Cost of goods/average inventory
Cost of goods sold = $50000
Average inventory = beginning of inventory + ending inventory/2
Average inventory = $16000+$20000/2
Average inventory = $36000/2
Average inventory = $18000
Inventory turn over = $50000/$18000
Inventory turn over= 2.78
A car is discounted 10% and sells for $15,673. What was the discount amount?
Answer:
$1741.44
Step-by-step explanation:
The discounted amount is 100% -10% = 90% of the original. The amount of the discount is 10% of the original, or 1/9 of the discounted amount:
10% = 90% × 1/9
The discount was ...
$15,673/9 = 1,741.44
_____
Check
The original is the sum of the discounted amount and the discount:
original price = $15,673.00 +1,741.44 = $17, 414.44
10% of that value is 1,741.44, as shown above.
A voter receives a call in which the caller claims to be conducting a national opinion research poll. The voter is asked if his or her opinion about a congressional candidate would change if he or she knew that the candidate once had a car crash while driving under the influence of alcohol. Identify and explain at least one source of bias in the study described. Then suggest how the bias might have been avoided?
a. The data do not seem to support the claims being made by the study. The researcher should consult an expert to make sure that he or she is correctly interpreting the data.
b. The study does not appear to have a well-defined goal. The researcher should determine his or her goal and precisely define the variables of interest.
c. Since the sample is self-selected, there is a definite participation bias in this study. The researcher should randomly select the subjects of the study.
d. The wording of the question is biased to strengthen opposition against a particular candidate. The question wording should be changed to be more neutral.
Answer:
The correct answer is D. The wording of the question is biased to strengthen opposition against a particular candidate. The question wording should be changed to be more neutral.
Step-by-step explanation:
The phrasing and setup of the poll will produce responses that are biased against the candidate. The setup of the poll should be changed to avoid influencing the opinions of the respondents.
Suppose f(x) is continuous on [3,6] and −3≤f′(x)≤5 for all x in (3,6). Use the Mean Value Theorem to estimate f(6)−f(3).
Answer: -9 ≤ f(6) - f(3) ≤ 15
Step-by-step explanation:
In order to use the Mean Value Theorem, it must be continuous and differentiable. Both of these conditions are satisfied so we can continue.
Find f(6) - f(3) using the following formula:
[tex]f'(c)=\dfrac{f(b)-f(a)}{b-a}[/tex]
Consider: a = 3, b = 6
[tex]\text{Then}\ f'(c)=\dfrac{f(6)-f(3)}{6-3}\\\\\\\rightarrow \quad 3f'(c)=f(6) - f(3)[/tex]
Given: -3 ≤ f'(x) ≤ 5
-9 ≤ 3f'(c) ≤ 15 Multiplied each side by 3
→ -9 ≤ f(6) - f(3) ≤ 15 Substituted 3f'(c) with f(6) - f(3)
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. Suppose that the mean income is found to be $18.5 for a random sample of 2253 people. Assume the population standard deviation is known to be $6.1. Construct the 98% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.
Answer:
= ( $18.2, $18.8)
Therefore, the 98% confidence interval (a,b) = ( $18.2, $18.8)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = $18.50
Standard deviation r = $6.10
Number of samples n = 2253
Confidence interval = 98%
z(at 98% confidence) = 2.33
Substituting the values we have;
$18.5+/-2.33($6.1/√2253 )
$18.5+/-2.33($0.128513644290)
$18.5+/-$0.299436791196
$18.5+/-$0.3
= ( $18.2, $18.8)
Therefore at 98% confidence interval (a,b) = ( $18.2, $18.8)
Here It Is !!
More Otw
Answer:
3
Step-by-step explanation:
0 pairs mean when two "boxes" add together to make 0. For the x's we only have one because x + (-x) = x - x = 0. For the other ones we have two (the + means 1 and the - means -1) because 1 + (-1) = 1 - 1 = 0. Therefore the answer is 1 + 2 = 3.
A toy car is placed on the floor He moves in a straight line starting from rest and travels with a constant acceleration for three seconds reaching a velocity of 4 meters per second it then slows down with constant deceleration of 0.5 meters per second squared For four seconds before hitting the wall and stopping draw a velocity time graph for the toy car what is the total distance travelled by the toy car
Answer:
18 meters.
Step-by-step explanation:
There is a constant acceleration for 3 seconds, reaching 4 m/s. This, when drawn on a velocity/time graph, creates a diagonal line. The area underneath this line, which is the distance it travels, is found by the following: 0.5(l*h), the formula used to find the area of a triangle.
0.5(3*4)=6m
There is then a constant deceleration of 0.5m/s for 4 seconds. This does also create a diagonal line on a velocity/time graph, but it doesn't go down to 0. What I do is split it up so that a triangle and a rectangle are created from the shape made. The triangle has a height of 2, and a length of 4, so we use the same formula used before.
0.5(2*4)=4m
Now, all that remains is a rectangle of height 2 and a length of 4, so we find the area of it.
2*4=8m
Finally, we add each of these up.
6m+4m+8m=18m
Sorry if the step by step process was poorly explained, I'm not the best at explaining. Hope this helped, though. :^)
The total distance traveled by the toy car is 18 meters.
What is acceleration?Acceleration of any object is defined as the variation in the speed of the object with the variation of time. Acceleration is a vector term and to define it we require both the magnitude and the direction. The unit of acceleration can be m / sec², miles / sec², etc.
For three seconds, there is a steady acceleration that reaches 4 m/s. This yields a diagonal line when drawn on a velocity/time graph. The following formula can be used to determine the region beneath this line, or the distance it travels:
The triangle area is calculated using the formula:-
A = 0.5(l x h).
A = 0.5(3 x 4)=6m
There is then a constant deceleration of 0.5m/s for 4 seconds. This does also create a diagonal line on a velocity/time graph, but it doesn't go down to 0. What I do is split it up so that a triangle and a rectangle are created from the shape made. The triangle has a height of 2, and a length of 4, so we use the same formula used before.
0.5(2 x 4)=4m
Now, all that remains is a rectangle of height 2 and a length of 4, so we find its area of it.
2 x 4 = 8m
Finally, we add each of these up.
6m+4m+8m=18m
Therefore, the total distance traveled by the toy car is 18 meters.
To know more about acceleration follow
https://brainly.com/question/23516420
#SPJ2
Solve the problem. When going more than 38 miles per hour, the gas mileage of a certain car fits the model where x is the speed of the car in miles per hour and y is the miles per gallon of gasoline. Based on this model, at what speed will the car average 15 miles per gallon? (Round to nearest whole number.)
Answer:
73 mph
Step-by-step explanation:
The question seems to be incomplete because the model is missing, I found a similar question with the addition of the model, so if we can solve it (see attached image).
We have that the model would be:
y = 43.81 - 0.395 * x
We need to solve for x, if y = 15
Replacing:
15 = 43.81 - 0.395 * x
Solving for x we have:
0.395 * x = 43.81 - 15
0.395 * x = 28.81
x = 28.81 / 0.395
x = 72.9
We are asked to round to the nearest number therefore x = 73.
The car will average 15 miles per gallon at the speed of 73 miles per hour.
If the figures below are similar, find the scale factor of Figure B to Figure A.
48
27
60
А
16
B
20
9
Answer:
The scale factor is 3.
Step-by-step explanation
Figure B has side measures 16, 20, and 9. Figure A has side measures 48, 27, and 60. The ratio of each of the corresponding sides is 1:3 (16:48, etc). Therefore, the scale factor of Figure B to Figure A is 3.
Alguien me puede ayudar con esto por favor!!!!
Answer:
8 + 15i
Step-by-step explanation:
(-2 + 3i) + 2(5 + 6i) =
= -2 + 3i + 10 + 12i
= 8 + 15i
whats the percentage of 56/100
Answer:
56%
Step-by-step explanation:
Any number out of 100 is that number's percent.
If it's for say 0.1/100, its 0.1%.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
The correct answer would be A
(I am not guessing I had the same quiz before)
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A. -6 ≤ y ≤ 9
Step-by-step explanation:
→Looking at the graphed function, you can see that the line starts at when y = -6. Then the function slowly increases, until it finally stops when y = 9.
→This means that the range (y-values) of the function can be from -6 through 9.
The correct answer should be "A. -6 ≤ y ≤ 9."
Angle 6= (11x+8) and angle 7=(12x-4) what is the measure of angle 4
Answer:
Answer is m∠4=40
Step-by-step explanation:
take note that m∠6 & m∠7 are vertical angles. Vertical angles are equal to each other, therefore m∠6 is equal to m∠7.
m∠6 = m∠7 (vertical angles)
11x + 8 = 12x – 4
12x - 11x = 8 + 4
x = 12
so
m∠6 = 11x + 8
m∠6 = 11(12) + 8
m∠6 = 132 + 8
m∠6 = 140
m∠4 = 180 - m<6
m∠4 = 180 - 140
m∠4 = 40
Answer:
A
Step-by-step explanation: Took test
What should I buy? A study conducted by a research group in a recent year reported that of cell phone owners used their phones inside a store for guidance on purchasing decisions. A sample of cell phone owners is studied. Round the answers to four decimal places.
Answer:
The probability that seven or more of them used their phones for guidance on purchasing decisions is 0.7886.
Step-by-step explanation:
The question is incomplete:
What should I buy? A study conducted by a research group in a recent year reported that 57% of cell phone owners used their phones inside a store for guidance on purchasing decisions. A sample of 14 cell phone owners is studied. Round the answers to at least four decimal places. What is the probability that seven or more of them used their phones for guidance on purchasing decisions?
We can model this as a binomial random variable, with p=0.57 and n=14.
[tex]P(x=k)=\dbinom{n}{k} p^{k}q^{n-k}[/tex]
a) We have to calculate the probability that seven or more of them used their phones for guidance on purchasing decisions:
[tex]P(x\geq7)=\sum_{k=7}^{14}P(x=k)\\\\\\[/tex]
[tex]P(x=7)=\dbinom{14}{7} p^{7}q^{7}=3432*0.0195*0.0027=0.1824\\\\\\P(x=8) = \dbinom{14}{8} p^{8}q^{6}=3003*0.0111*0.0063=0.2115\\\\\\P(x=9) = \dbinom{14}{9} p^{9}q^{5}=2002*0.0064*0.0147=0.1869\\\\\\P(x=10) = \dbinom{14}{10} p^{10}q^{4}=1001*0.0036*0.0342=0.1239\\\\\\P(x=11) = \dbinom{14}{11} p^{11}q^{3}=364*0.0021*0.0795=0.0597\\\\\\P(x=12) = \dbinom{14}{12} p^{12}q^{2}=91*0.0012*0.1849=0.0198\\\\\\P(x=13) = \dbinom{14}{13} p^{13}q^{1}=14*0.0007*0.43=0.004\\\\\\[/tex]
[tex]P(x=14) = \dbinom{14}{14} p^{14}q^{0}=1*0.0004*1=0.0004\\\\\\[/tex]
[tex]P(x\geq7)=0.1824+0.2115+0.1869+0.1239+0.0597+0.0198+0.004+0.0004\\\\P(x\geq7)=0.7886[/tex]