Answer:
We have to flip the coin 78 times.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
We suspect that the coin is fair.
This means that [tex]\pi = 0.5[/tex]
96.5% confidence level
So [tex]\alpha = 0.035[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.035}{2} = 0.9825[/tex], so [tex]Z = 2.108[/tex].
How many times would we have to flip the coin in order to obtain a 96.5% confidence interval of width of at most .12 for the probability of flipping a head?
n times, and n is found when M = 0.12. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.12 = 2.108\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.12\sqrt{n} = 2.108*0.5[/tex]
[tex]\sqrt{n} = \frac{2.108*0.5}{0.12}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.108*0.5}{0.12})^2[/tex]
[tex]n = 77.1[/tex]
Rounding up
We have to flip the coin 78 times.
According to the AAA Foundation for Traffic Safety's American Driving Survey, U.S. drivers spend.
on average, 51 minutes behind the wheel each day. A researcher believes this is an overstatement.
To investigate, a random sample of 75 drivers were selected. The study revealed that the mean
time behind the wheel for the sample of 75 drivers was 46.4 minutes with a standard deviation of
18.8 minutes. Is there convincing evidence that the mean time behind the wheel for all U.S. drivers
is less than 51 minutes? Use a = 0.01.
Answer:
The pvalue of the test is 0.017 > 0.01, which means that there is not convincing evidence that the mean time behind the whell for all U.S drivers is less than 51 minutes.
Step-by-step explanation:
U.S. drivers spend on average, 51 minutes behind the wheel each day.
This means that at the null hypothesis we test that:
[tex]H_{0}: \mu = 51[/tex]
Is there convincing evidence that the mean time behind the wheel for all U.S. drivers is less than 51 minutes?
This means that the alternate hypothesis is:
[tex]H_{a}: \mu < 51[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
51 is tested at the null hypothesis:
This means that [tex]\mu = 51[/tex]
The study revealed that the mean time behind the wheel for the sample of 75 drivers was 46.4 minutes with a standard deviation of 18.8 minutes.
This means that [tex]n = 75, X = 46.4, \sigma = 18.8[/tex]
Value of the test-statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{46.4 - 51}{\frac{18.8}{\sqrt{75}}}[/tex]
[tex]z = -2.12[/tex]
Pvalue of the test:
The pvalue of the test is the probability of finding a sample mean less than 46.4, which is the pvalue of z when X = 46.4.
Looking at the z-table, z = -2.12 has a pvalue of 0.017.
Decision:
The pvalue of the test is 0.017 > 0.01, which means that there is not convincing evidence that the mean time behind the whell for all U.S drivers is less than 51 minutes.
No, there isn't convincing evidence that the mean time behind the wheel for all U.S. drivers is less than 51 minutes.
Given the following data:
Mean = 51.Number of drivers = 75 drivers.Sample mean (mean time) = 46.4 minutes.Standard deviation = 18.8 minutes.What is a null hypothesis?A null hypothesis ([tex]H_0[/tex]) can be defined the opposite of an alternate hypothesis ([tex]H_a[/tex]) and it asserts that two (2) possibilities are the same.
For the null hypothesis, we would test that:
[tex]H_o : \mu =51[/tex]
For the alternate hypothesis, we would test that:
[tex]H_a : \mu < 51[/tex]
The test statistics would be calculated with this formula:
[tex]Z=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]
Where:
x is the sample mean.u is the mean.[tex]\delta[/tex] is the standard deviation.n is the number of drivers.Substituting the given parameters into the formula, we have;
[tex]Z=\frac{46.4\;-\;51}{\frac{18.8}{\sqrt{75} } }\\\\Z=\frac{-4.6}{\frac{18.8}{8.6603} }\\\\Z=\frac{-4.6}{2.1708 }[/tex]
Z = -2.12.
What is a p-value?In Statistics, a p-value also known as the probability value is the probability which occurs when the null hypothesis ([tex]H_0[/tex]) is true of obtaining a sample mean that is at least as unlikely as what is observed by a researcher or scientist.
From the z-table, a z-score of -2.12 corresponds to or has a p-value of 0.017. Therefore, the p-value for this test is 0.017 > 0.01.
In conclusion, there isn't convincing evidence that the mean time behind the wheel for all U.S. drivers is less than 51 minutes.
Read more on null hypothesis here: https://brainly.com/question/14913351
12. Find the measure of angle x.
13. Find the measure of angle x.
Answer:
x=21
x=122
Step-by-step explanation:
Answer:
x= 21
x=122
I hope this will help you.
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 410 gram setting. It is believed that the machine is underfilling the bags. A 22 bag sample had a mean of 408 grams with a standard deviation of 14. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled
Answer:
i think it is 451 i believe
Need ASAP
Gabe spent 26 days traveling in Europe. How many hours did he spend traveling in Europe?
Answer:
624hours
Step-by-step explanation:
There are 24 hours in a day, so multiply the amount of days by 24 to find the amount of hours:
26 x 24 = 624hours
PLEASE HURRY
A public radio station raised 25% more during this year's fund-
raiser than it raised last year. If p represents the amount raised
by last year's fund-raiser, which expression represents the
amount raised this year?
Answer:
1.25p
Step-by-step explanation:
p = amount raised last year
amount raised this year = p +(25% of p)
=1 p+0.25p
=p(1+0.25)
=1.25p
A container has a volume of 3.6 m3 . Convert the volume into cm3 .
Answer: 3 600 000 cm³
Step-by-step explanation: 1 m³ = 1000 dm³ = 1 000 000 cm³
In ΔKLM, m = 480 cm, k = 360 cm and ∠L=29°. Find the area of ΔKLM, to the nearest square centimeter.
Answer:
The answer is=
41887.551
Use the point-slope form to write an equation of a line through the given points.
(−3, 2) and (3, 4)
Answer:
y-2=1/3(x+3)
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(4-2)/(3-(-3))
m=2/(3+3)
m=2/6
simplify
m=1/3
y-y1=m(x-x1)
y-2=1/3(x-(-3))
y-2=1/3(x+3)
What is the perimeter of the shaded part of this??
Answer:
18.9cm ( I rounded of and used Π as 3.14)
Step-by-step explanation:
P=distance all round
=1\2ΠD +Πd
see you have to calculate the upper length of the circle , since its half u multiply by a half. And since its not fully shaded the two semi circles are now included as the lower part of the whole shape. so you add them too. (I hope I'm making sense)
solve it : x² *dy/dx = -2y
Answer:
r= -sec(θ) x ∛2
θ=0
Step-by-step explanation:
Which expressions are equivalent to 16^(3/2)?
Answer:
16^(3/2)=64
Step-by-step explanation:
In the book Chances: risk and odds in Everyday Life, author James Burke says that approximately 57% of the general US population wears glasses or contacts. If two people are chosen at random from the US population, what is the probability that both wear glasses or contacts?
Answer:
[tex]Pr = 32.49\%[/tex]
Step-by-step explanation:
Given
Let E represents the event of wearing glasses or contacts.
So;
[tex]P(E) =57\%[/tex]
Required
The probability that selected 2 wears glasses
This is calculated as:
[tex]Pr = P(E)\ and\ P(E)[/tex]
[tex]Pr = P(E)\ *\ P(E)[/tex]
[tex]Pr = 57\% * 57\%[/tex]
[tex]Pr = 0.57 * 0.57[/tex]
[tex]Pr = 0.3249[/tex]
[tex]Pr = 32.49\%[/tex]
Hall and rey are seeing who can make the most money working their new summer jobs. Rey made $154.21 in the first month. If hall finishes the summer with $313.06, how many hours at a rate of $8.04 per our, does rey need to work to make more than hall
Write an inequality that represents the situation using x to represent the hours
Answer:
x564.99
Step-by-step explanation:
Show
that (2+√3)(2-√3)(5+root2)
(5-root2) is rational number.
Answer:
(2+3)(2−3)(5+2)(5−2)=>(22−(3)2)(52−(22))=>(4−3)(25−2)=>(1)(23)=>23
max is a 22 year old planning to retire at age 67 he is i vesting in a mutual fund and hopes to earn the average inflation adjusted stock market return of 7% anually. If max deposits $200 per month into this fund, how much can he expect to have when he retires? Show work
Based on the calculation below, the amount Max can be expected to have when he retires is $758,518.94.
How to calculate the future value (FV)?The amount he will be expected to have when he retires can be calculated using the formula for calculating the future value of an ordinary annuity as follows:
FV = D * (((1 + r)^n – 1) / r) ……………………………….. (1)
Where;
FV = Future value or the expected amount when he retires = ?
D = Monthly deposit = $200
r = monthly average inflation adjusted stock market return = 7% / 12 = 0.07 / 12 = 0.00583333333333333
n = number of months = (67 - 22) * 12 = 540
Substituting the values into equation (1), we have:
FV = $200 * (((1 + 0.00583333333333333)^540 – 1) / 0.00583333333333333)
FV = $758,518.94
Learn more about future value here: https://brainly.com/question/14586629.
#SPJ1
Which property can be used to solve the equation?
d/10=12
A. addition property of equality
B. subtraction property of equality
C. multiplication property of equality
D. division property of equality
Answer:
C
Step-by-step explanation:
You are dividing, if you think about it every time I do it is the opposite of your equation. Plus you are supposed to multiply on both sides to get the value of d.
5/x=7/x-4
pls help me with this problem if u help i willl heart and follow you
Answer:
5/x = 7/x-4
5(x-4) = 7(x)
5x - 20 = 7x
5x - 7x = 20
-2x = 20
x = -20/2 = -10
What is the solution to the equation?
19 + 13x = 32
Record your answer in the boxes
below.
00000.00
+/-
I give brainleist
Answer:
the answer is x=1
Step-by-step explanation:
minus 19 on both sides
then divide by 13 on both sides
Which of the following is the measure of an acute angle?
A. 89°
B. 270°
C. 97°
D. 122°
Answer:
A
Step-by-step explanation:
An acute angle is an angle that is less than 90 degrees.
Answer:
Step-by-step explanation:
A
1 = 5cm base s = 8cm s= 8cm 1 = q cm
what is surface area
Answer:
The surface of the area is 320 cm. :D
Step-by-step explanation:
Type the correct answer in the box log's
Answer:
log(7) will be the correct answer.
Step-by-step explanation:
[tex]\text{\frac{14}{3}}+\text{log}(\frac{11}{5})-\text{log}(\frac{22}{15})[/tex]By using law of logarithm to solve the given expression,
1). [tex]\text{log}(m)+\text{log}(n)=\text{log(mn)}[/tex]
2). [tex]\text{log(m)}-\text{log(n)}=\text{log}(\frac{m}{n})[/tex]
By applying these rules, we can simplify the given expression,
[tex]\text{log}(\frac{14}{3})+\text{log}(\frac{11}{5})-\text{log}(\frac{22}{15})[/tex]
[tex]\text{log}(\frac{14}{3})+\text{log}(\frac{11}{5})-\text{log}(\frac{22}{15})=\text{log}(\frac{\frac{14}{3}\times \frac{11}{5}}{\frac{22}{15}})[/tex]
[tex]=\text{log}(\frac{\frac{154}{15}}{\frac{22}{15}})[/tex]
= [tex]\text{log}(\frac{154}{15}\times \frac{15}{22})[/tex]
= log(7)
Therefore, log(7) will be the correct answer.
What is the product of 2.416 and 10^5? *
Answer:
241600
Step-by-step explanation:
Mike, Tania, Bill, and Rachael each took many samples from the same
population of students. The number of students in each sample is shown in
the table. Which person's sampling distribution is most likely to closely
approximate the population distribution?
Person taking samples Students in each sample
Mike
79
Tania
23
Bill
37
Rachael
51
A. Tania
B. Mike
C. Bill
D. Rachael
Answer: Mike!
Step-by-step explanation:
what is the equation for the volume of a cylinder? I think is v=pi × r^2 * h just asking for clarification
Answer:
V=pi multiplied by r^2 times height
Step-by-step explanation:
What should be included in a financial plan to protect assets?
Is 2/9 a perfect square
Reflect (2.5,4.5) in the x-axis.
9514 1404 393
Answer:
(2.5, -4.5)
Step-by-step explanation:
Reflection in the x-axis changes the sign of the y-coordinate
(x, y) ⇒ (x, -y)
(2.5, 4.5) ⇒ (2.5, -4.5)
How is the graph of the parent quadratic function transformed to produce the graph of y--(2x+6)2+3?
O The graph is compressed horizontally by a factor of 2, shifted left 3 units, reflected over the x-axis, and translated
up 3 units
O The graph is reflected over the x-axis, compressed horizontally by a factor of 2, shifted left 6 units, and translated
up 3 units
The graph is stretched horizontally by a factor of 2, reflected over the x-axis, shifted left 3 units, and translated up
3 units
O The graph is reflected over the x axis, stretched horizontally by a factor of 2, shifted left 6 units, and translated up
3 units
Answer: a
Step-by-step explanation:
just took the test
300 paper cups in a dispenser the cups are taken from dispenser at rate at rate of 40 cups per hour
Answer:
i dont know i dont understand the question
PLEASE HELP!!!!!! I WILL MARK YOU BRAINIEST
Answer:
Measure of angle b is 42 degrees
Step-by-step explanation:
Since angle b is part of a right angle, we can see that part of the right and blue is 48 degrees, and the other part is b. So, we can do 90-48 to get 42 degrees.
Answer:
42
Step-by-step explanation:
since one of the lines for angle b makes a 90° angle all you have to do is subtract 48 from 90 and that is your answer