Answer:
The expected revenue is $984.6.
Step-by-step explanation:
The tourist operator sells 21 non-refundable tickets, as the tourist may not show up.
The tourist have a probability of 0.02 of not showing up, independent of each other.
The income is the selling of the 21 tickets at $50 each.
[tex]I=21*50=1,050[/tex]
The only cost considered in this problem is the refund if a tourist show up and a seat is not available.
This only happens when the 21 tourists show up. If each tourist has a probability of 0.02 of not showing up, they have a probability of 0.98 of showing up.
For the event that the 21 tourists show up, we have the probability:
[tex]P=0.98^{21}\approx0.654[/tex]
For each of this event, the tour operator has to pay $100, so the expected revenue of the tour operator is:
[tex]E(R)=I-E(C)=1,050-0.654\cdot 100=1,050-65.4=984.6[/tex]
Keep gettin this one wrong please help
Answer:
30 Nickels and 188 Pennies
Step-by-step explanation:
okay, so to set up the equation first, we have to assign each coin a variable, let's call them p and n:
P= number of pennies
N= number of nickels
the value of a penny is 1 cent, so 1P, and the value of a nickel is 5 cents, so 5N
The problem states that he has 218 coins, meaning that the total number of pennies and nickels adds up to 218:
P + N = 218
the total value of the coins is $3.38, so that would mean that 1P + 5N has to equal $3.38:
1P + 5N = 338
Okay, so now that we have our equations let's solve them using elimination:
we have to get a common coefficient between both equations, so let's multiply our first equation by 5:
P x 5 = 5P
N x 5 = 5N
218 x 5 = 1090
so, now we can solve by elimination:
5P + 5N = 1090
1P + 5N = 338
the N's cancel out:
4P = 752
divide both sides by 4:
P = 188
okay, so if theres a total of 218 coins, subtract 188 from 218:
218 - 188 = 30
so, there are 30 nickels and 188 pennies.
check our work:
5 x 30 = 150
1 × 188 = 188
150 + 188 = 338
338 = 338
I hope this helps! :)
what would be the answer for this.
Answer & Step-by-step explanation:
We are given that m∠1 = m∠2. We are to prove that line l is parallel to line m. So, let's make a proof. Your first statement should always be the given statement. You are given the statements. All we have to do is find the reasons for those statements.
m∠1 = m∠2 → Givenm∠1 = m∠3 → Vertical angles are equalm∠2 = m∠3 → Substitutionl ║m → If corresponding angles are equal, then lines are parallelAt a school fair, each student spins the spinner, which is equally likely to land on each of the four sectors. The spinner shows how many tokens the student wins or loses. What is the expected number of tokens that a student will win on each spin
Answer:
3 tokens.
Step-by-step explanation:
We need the roulette image, therefore we will suppose one that I will leave as an attached image:
The main thing to keep in mind in this case is that the probabilities are the same, therefore you don't have to take that into account, just operate with the values of each sector, therefore the expected value would be:
expected value = profit - loss
expected value = (5 + 5) - (4 + 3)
expected value = 10 - 7 = 3
This means that the number of tokens waiting for the student to earn for each spin is 3 tokens.
Find the point on the curve r(t) = (5Sint)i + (5Cost)j +12tk
at a distance 26pi units along the curve from the point (0,5,0) inthe direction of increasing arc length.
Answer:
Find the point on the curve r(t) = (5Sint)i + (5Cost)j +12tk
at a distance 26pi units along the curve from the point (0,5,0) inthe direction of increasing arc length.
(My attempt):
T comes to be 2pi and when the integral is done and solved to givea value of 26pi and the position comes to be (0,5,24pi). However,this calculation and answer though correct (according to the backof the book) does not involve the use of the fact that at time t=0,the particle is at (0,5,0).
What for is that information given then?
Step-by-step explanation:
Consider the curve r(t) = (5Sint)i + (5Cost)j + (12t)k
Need to find the point on the given curve at a distance 26π unit along the curve from the point (0,5,0) inthe direction of increasing arc length.
Length of a smooth curve is [tex]r(t)=x(t)i+y(t)j+z(t)k, \ \ a\leq t\leq b[/tex] that is traced exactly once as t increase from t = a to t = b, is
[tex]L=\int\limits^b_a \sqrt{(\frac{dx}{dt} )^2+(\frac{dy}{dt} )^2+(\frac{dz}{dt} )^2dt}[/tex]
For the given curve
x(t) = 5 sin t
y(t) = 5 cos t
z(t) = 12t
When t = 0
x(0) = 5 sin 0
= 0
y(0) = 5 cos 0
= 0
z(0) = 12(0)
=0
So, the point (0, 5, 0) corresponds to t = 0
So let t = t₀ correspond to any point (x, y, z) on the curve at a distance of 26pi units from the point t = 0 along the increasing arc length
So, the length of curve from the point t = 0 to t = t₀ is L = 26pi units
Substitute the known value to the arc length formula
[tex]L=\int\limits^b_a \sqrt{(\frac{dx}{dt} )^2+(\frac{dy}{dt} )^2+(\frac{dz}{dt} )^2dt}[/tex]
[tex]26\pi=\int\limits^{t_0}\sqrt{(5 \cos t)6+(-5 \sin t)^2+(12)^2dt}\\\\26\pi=\int\limits^{t_0}_0\sqrt{25 \cos ^2t+25 \sin ^2t+144dt} \\\\26\pi=\int\limits^{t_0}_0 \sqrt{25(\cos^2t+ \sin^2t)+144dt}\\\\26\pi=\int\limits^{t_0}_0\sqrt{25(1)+144dt} \\\\26\pi= \int\limits^{t_0}_0\sqrt{169dt} \\\\26\pi= \int\limits^{t_0}_013 dt\\\\26\pi=13\int\limits^{t_0}_0dt\\\\26\pi=13[t]^{t_0}_0\\\\26\pi=13[t_0-0]\\\\26\pi=13t_0\\\\t_0=\frac{26\pi}{13} \\\\t_0=2\pi[/tex]
The point corresponding to [tex]t_0 = 2\pi[/tex]
when t = 0
[tex]x(2\pi)=5 \sin (2\pi)\\\\=0\\\\y(2\pi)=5 \cos (2\pi)\\\\=5(1)=5\\\\z(2\pi)=12(2\pi)\\\\=24\pi[/tex]
Therefore the point corresponding to [tex]t_0 = 2\pi[/tex] is [tex](0,5,24\pi)[/tex]
Hence, the required point on the given curve at distance 26\pi units along the curve from the point (0,5,0) in the direction of increasing arc length is [tex](0,5,24\pi)[/tex]
Please answer this correctly
Answer:
42 13/20 km
Step-by-step explanation:
10 3/10+9 7/20+14 7/10+ 8 9/20=41+ (6+7+14+9)/20=41 + 1 13/20= 42 13/20 km
Could someone please give me the answer to this?
Answer:
? = 8.77
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opposite/ hypotenuse
sin 20 = 3/?
? = 3 / sin 20
? =8.7714132
To the nearest hundredth
? = 8.77
We can use the trigonometric function [ sin theta = opposite/hypotenuse ] to solve.
sin(20) = 3/hypotenuse
hypotenuse = 3/sin(20)
hypotenuse = 8.7714...
Round to the nearest hundredth.
8.7714... → 8.77
Therefore, the answer is 8.77
Best of Luck!
A worker is paid $2,350 monthly and has $468 withheld from each monthly paycheck. Which of the following is her annual net salary
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
B. -4<x<2
Step-by-step explanation:
The highest x point is -4 and lowest peak is 2
Answer:
B. -4 ≤ x ≤ 2
Step-by-step explanation:
→Basically, the question is asking, "At what point is the line on the graph decreasing?"
→Looking at the graph, you can see that when x = -4, that's when the line on the graph starts to decrease. The line continues to decrease, until it reaches the point where x = 2.
This makes the correct answer "B. -4 ≤ x ≤ 2."
The formula in cell B1 is= A$2. Autofill is used by dragging B1’s autofill box across to C1,D1, and E1. What formulas will appear in C1, D1, and E1, respectively?
Answer:
The formulas that will appear in
C1 is =B$2
D1 is = C$2
E1 is = D$2
Step-by-step explanation:
Given
Formula in B1 is = A$2
Required
Formulas in C1, D1 and E1 when dragged from B1.
In Microsoft Office Excel, this is called absolute reference.
But this type of absolute reference requires that only the cell name will be changed or altered, the row number will always remain the same no matter where it's been dragged to.
Since the initial column name is A and the Initial row number is 2 (from A$2),
Cell C1 will take the formula = B$2
Cell D1 will take = C$2
Cell E1 will take = D$2
Notice that only the column name changed for each formula; the row number remain unchanged.
Answer:
=B$2, C$2, D$2
Step-by-step explanation:
Find the roots of the quadratic equation 3y² - 4y+1=0 By
i) completing the square method
ii) the formula
Answer:
i) [tex] 3y^2 -4y +1=0[/tex]
We can divide both sides of the equation by 3 and we got:
[tex] y^2 -\frac{4}{3}y +\frac{1}{3}=0[/tex]
Now we can complete the square and we got:
[tex] (y^2 -\frac{4}{3}y +\frac{4}{9}) +(\frac{1}{3} -\frac{4}{9})=0[/tex]
[tex] (y- \frac{2}{3})^2 =\frac{1}{9}[/tex]
We take square root on both sides and we got:
[tex] y-\frac{2}{3}= \pm \frac{1}{3}[/tex]
And the solutions for y are:
[tex] y_1 = \frac{1}{3} +\frac{2}{3}=1[/tex]
[tex] y_1 = -\frac{1}{3} +\frac{2}{3}=\frac{1}{3}[/tex]
ii) [tex] y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
And with [tex] a = 3, b=-4 and c =1[/tex] we got:
[tex] y =\frac{4 \pm \sqrt{(-4)^2 -4(3)(1)}}{2*3}[/tex]
And we got:
[tex] y_1 = 1 , y_2 =\frac{1}{3}[/tex]
Step-by-step explanation:
Part i
For this case we have the following function given:
[tex] 3y^2 -4y +1=0[/tex]
We can divide both sides of the equation by 3 and we got:
[tex] y^2 -\frac{4}{3}y +\frac{1}{3}=0[/tex]
Now we can complete the square and we got:
[tex] (y^2 -\frac{4}{3}y +\frac{4}{9}) +(\frac{1}{3} -\frac{4}{9})=0[/tex]
[tex] (y- \frac{2}{3})^2 =\frac{1}{9}[/tex]
We take square root on both sides and we got:
[tex] y-\frac{2}{3}= \pm \frac{1}{3}[/tex]
And the solutions for y are:
[tex] y_1 = \frac{1}{3} +\frac{2}{3}=1[/tex]
[tex] y_1 = -\frac{1}{3} +\frac{2}{3}=\frac{1}{3}[/tex]
Part ii
We can use the quadratic formula:
[tex] y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
And with [tex] a = 3, b=-4 and c =1[/tex] we got:
[tex] y =\frac{4 \pm \sqrt{(-4)^2 -4(3)(1)}}{2*3}[/tex]
And we got:
[tex] y_1 = 1 , y_2 =\frac{1}{3}[/tex]
Joe and Janna leave home at the same time, traveling in opposite directions. Joe
drives 45 miles per hour and Janna drives 40 miles per hour. In how many hours will
they be 510 miles apart?
O a) 7 hours
Ob) 6 hours
Oc) 4 hours
Od) 5 hours
Answer:
B
Step-by-step explanation:
because if you do 40 times 6 and 45 times 6 you get 270 and 240 and you add them up for 510
(8x^3 + x^2 - 5) / (x-6)
Answer:
the answer is 8x^2+49x+294+1759/x-6
f(x)=4x-8 and g(x)=5x+6, find (f+g)(x)
Answer:
9x-2
Step-by-step explanation:
Since you are adding the two functions, you should first start adding like terms. 4x + 5x is 9x. -8 + 6 is -2. Thus the value of (f+g)(x) is 9x-2.
The marked price of a water cooler is $ 500. The shopkeeper offers an off-season discount of 15% on it. Find the discount.
Answer:
75 dollars
Step-by-step explanation:
You know that 500=100%, so we can set up the following
15%(500/100%) = 75
so the discount 75 dollars
Is the sequence arithmetic? (Yes or no) If yes, please also give its common difference. 14) -2.8, -2.2, -1.6, -1.0
Answer:
Yes
The common difference is .6
Step-by-step explanation:
Take the second term and subtract the first term
-2.2 - (-2.8)
-2.2+ 2.8 = .6
Take the third term and subtract the second
-1.6 - (-2.2)
1.6 +2.2
The common difference is .6
Answer:
Yes
Step-by-step explanation:
-2.8, -2.2, -1.6, -1.0
-2.2-(-2.8)= -1.6 - (-2.2)= -1 - (-1.6)= 0.6
This is AP with first term -2.8 and common difference 0.6
Suppose you work for the Department of Natural Resources and you want to estimate, with 95% confidence, the mean (average) length of all walleye fingerlings in a fish hatchery pond. You take a random sample of 36 fingerlings and determine that the average length is 7.4 inches and the population standard deviation is known to be 1.9 inches.
a. Construct a 95% confidence interval.
b. Interpret the Confidence Interval:
c. If the hatchery supervisor claimed that the average length of the walleye fingerlings fish is more than 7.5 inches, would you agree or disagree?
Answer:
a) [tex]7.4-1.96\frac{1.9}{\sqrt{36}}=6.78[/tex]
[tex]7.4+1.96\frac{1.9}{\sqrt{36}}=8.02[/tex]
b) For this case we can conclude that at 95% of confidence the true mean for the lenght of all welleye fingerprints in a fish hatchery pond is between 6.78 and 8.02
c) For this case since the value of 7.5 is included in the confidence interval we don't have enough evidence to conclude that the true mean is actually higher than 7.5 inches
Step-by-step explanation:
Information given
[tex]\bar X=7/4[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=1.9[/tex] represent the population standard deviation
n=36 represent the sample size
Part a
The confidence interval for the mean is given by :
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
The Confidence is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value would be [tex]z_{\alpha/2}=1.96[/tex]
Replacing the info we got:
[tex]7.4-1.96\frac{1.9}{\sqrt{36}}=6.78[/tex]
[tex]7.4+1.96\frac{1.9}{\sqrt{36}}=8.02[/tex]
Part b
For this case we can conclude that at 95% of confidence the true mean for the lenght of all welleye fingerprints in a fish hatchery pond is between 6.78 and 8.02
Part c
For this case since the value of 7.5 is included in the confidence interval we don't have enough evidence to conclude that the true mean is actually higher than 7.5 inches
Suppose you have a sample of 27 Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups, and who have an average gestation length of 17.4 days and a sample variance of 33.7 days. You want to test the hypothesis that Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups have a different gestation length than all Syrian hamsters.
Required:
Calculate the t- statistics.
Answer:
Test statistic t=1.2531.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups have a different gestation length than all Syrian hamsters (P-value=0.11).
Step-by-step explanation:
The question is incomplete: We need the gestation length of the population to perform the hypothesis test. We assume it to be 16 days (μ=16).
This is a hypothesis test for the population mean.
The claim is that Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups have a different gestation length than all Syrian hamsters.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=16\\\\H_a:\mu> 16[/tex]
The significance level is 0.05.
The sample has a size n=27.
The sample mean is M=17.4.
The sample variance is s^2=33.7 days^2.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=33.7^(0.5)=5.81.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{5.81}{\sqrt{27}}=1.1172[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{17.4-16}{1.1172}=\dfrac{1.4}{1.1172}=1.2531[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=27-1=26[/tex]
This test is a right-tailed test, with 26 degrees of freedom and t=1.2531, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t>1.2531)=0.11[/tex]
As the P-value (0.11) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups have a different gestation length than all Syrian hamsters.
A study found that 25% of car owners in Fiji had their cars washed professionally rather than do it themselves. If 18 carowners are randomly selected, find the probability that atmost two people have their cars washed professionally
Answer:
13.5%
Step-by-step explanation:
The probability of interest is the cumulative probability of a binomial probability density function with 18 trials and a probability of success of 0.25. We are interested in the value for x ≤ 2.
CalculatorSuch a calculation can be done "by hand" by adding up the probabilities for 0, 1, and 2 people. (A calculator is needed for the arithmetic.) One may as well use the appropriate function of a calculator to find the probability:
binomcdf(18, 0.25, 2) ≈ 0.135
The probability is about 13.5%.
A cone with radius 5 and height 12 has its radius doubled. How many times greater is the volume of the larger cone than the smaller cone? Use a pencil and paper. Explain how the volume of the cone would change if the radius were halved.
Answer:
[tex] V = \frac{1}{3} \pi (5)^2 (12)= 314.159[/tex]
Now if we increase the radius by a factor of 2 the new volume would be:
[tex] V_f = \frac{1}{3} \pi (2*5)^2 (12)= 1256.637[/tex]
And we can find the increase factor for the volume like this:
[tex] \frac{V_f}{V}= \frac{1256.637}{314.159}= 4[/tex]
Then if we increase the radius by 2 the volume increase by a factor of 4
If we reduce the radius by a factor of 2 then we will have that the volume would be reduced by a factor of 4.
On the figure attached we have an illustration for the cases analyzed we see that when we increase the radius the volume increase and in the other case decrease.
Step-by-step explanation:
For this case we have the following info given:
[tex]r = 5 , h =12[/tex]
and we can find the initial volume:
[tex] V = \frac{1}{3} \pi r^2 h[/tex]
And replacing we got:
[tex] V = \frac{1}{3} \pi (5)^2 (12)= 314.159[/tex]
Now if we increase the radius by a factor of 2 the new volume would be:
[tex] V_f = \frac{1}{3} \pi (2*5)^2 (12)= 1256.637[/tex]
And we can find the increase factor for the volume like this:
[tex] \frac{V_f}{V}= \frac{1256.637}{314.159}= 4[/tex]
Then if we increase the radius by 2 the volume increase by a factor of 4
If we reduce the radius by a factor of 2 then we will have that the volume would be reduced by a factor of 4.
On the figure attached we have an illustration for the cases analyzed we see that when we increase the radius the volume increase and in the other case decrease.
you invested $22,000 in two accounts paying 4% and 9% annual interest. if the total interest earned for the year was $1180, how much was invested at each rate
Answer:
Amount invested at 4% is $16,000
Amount invested at 9% is $6,000
Step-by-step explanation:
Let one vestment be x
if total investment is $22,000 then
other investment will $22,000 - x
simple interest earned in any year is given by
SI = p*r*t/100
where SI is the interest earned
t is the time period of investment
r is the rate of annual interest
_____________________________________
interest on one account 4%
p = x
t = 1 year
SI = x*4*1/100 = 4x/100
_____________________________
interest on one account 9%
p = 22,000 - x
t = 1 year
SI = (22,000 - x)*9*1/100 = (198000 - 9x)/100
_____________________________________
it is given that total interest earned was $1180
thus sum of SI calculated for the 9% and 4% investment will be equal to 1180
4x/100 + (198000 - 9x)/100 = 1180
=> (4x+198000 - 9x)/100 = 1180
=> 198000 - 5x = 1180*100
=> -5x = 118,000 - 198000
=> -5x = -80,000
=> x = -80,000/-5 = 16,000
Thus,
Amount invested at 4% is $16,000
Amount invested at 9% is $(22,000 - 16,000) = $6,000
Need Help With This:
The functions u and w are defined as follows. u(x)=2x-2 w(x)=-2x^2+1 Find the value of w(u(5)).
Answer:
-127
Step-by-step explanation:
u(x)=2x-2
w(x)= -2x^2+1
w(u(5))=?
---------
u(5)= 2*5-2= 8
W(8)= - 2*64+1= -127
Answer:
that was the wrong answer this site sucks
Quadrilateral QPRS is transformed by a dilation centered at the origin with a scale factor of 2 to create quadrilateral Q'P'R'S'. Which are the coordinates of quadrilateral Q'P'R'S'?
Q'(4, 4), P'(0, 0), R'(-4, -8), S'(8, -4)
Q'(1, 1), P'(0, 0), R'(-1, -2), S'(2, -1)
Q'(4, 4), P'(2, 2), R'(0, -2), S'(6, 0)
Q'(0, 0), P'(-2, -2), R'(-4, -6), S'(2, -4)
Answer:
B
Step-by-step explanation:
The coordinates of quadrilateral Q'P'R'S' is
Q'(4, 8), P'(0, 0), R'(-4, -8), S'(8, -4).
What is a scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object,
We have,
To perform a dilation centered at the origin with a scale factor of 2, we need to multiply the x and y coordinates of each vertex by 2.
So starting with the coordinates of quadrilateral QPRS:
Q(2, 4), P(0, 0), R(-2, -4), S(4, -2)
Multiplying each coordinate by 2, we get:
Q'(4, 8), P'(0, 0), R'(-4, -8), S'(8, -4)
Therefore,
The coordinates of quadrilateral Q'P'R'S' is
Q'(4, 8), P'(0, 0), R'(-4, -8), S'(8, -4).
Learn more about scale factors here:
https://brainly.com/question/20759556
#SPJ3
The complete question.
Quadrilateral QPRS is transformed by a dilation centered at the origin with a scale factor of 2 to create quadrilateral Q'P'R'S'. Which are the coordinates of quadrilateral Q'P'R'S'?
Where
The coordinates of PQRS are:
Q = (2, 4), P = (0, 0), R = (-2, -4), S = (4, -2).
The triangle shown below has an area of 16 units2.
Find z.
4
2
units
Answer:
8 units
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the base and h is the height
16 = 1/2 (4)*x
16 = 2x
Divide each side by 2
16/2 = 2x/2
8 =x
Need Help really difficult
A certain car traveling 34.0 mph skids to a stop in 29 meters from the point where the brakes were applied. In approximately what distance would the car stop had it been going 105.4 mph?
Answer:
279 m
Step-by-step explanation:
Work by friction = change in kinetic energy
Fd = ½ mv²
d ∝ v²
d / 29 m = (105.4 mph)² / (34.0 mph)²
d = 279 m
which fraction is the largest 5/7 7/10 10/13 show how u worked out the answer
Answer:
[tex]3.1/13[/tex]
Step-by-step explanation:
[tex]1.5/7 =0.214286[/tex]
[tex]2.7/10=0.27[/tex]
[tex]3.1/13 =0.238462[/tex]
Question:
Train A arrives at the station at 11:50 AM and leaves the station at 1:50 PM. How long does it stay in the station?
Make a Selection:
A. 1 hr
B. 2 hrs
C. 1 hr 25 min
D. 10 hrs
b/-3+4 is less than 13
Answer:
b < 13
Step-by-step explanation:
Idk what you're asking but I'll try.
[tex]\frac{b}{1}=b[/tex]
b < 13
Answer:
b > -27.
Step-by-step explanation:
b / -3 + 4 < 13
b/-3 < 13 - 4
b/-3 < 9
-b/ 3 < 9
Multiply both sides by -3 ( the inequality sign will flip):
b > -27
Spend some time looking at the vehicles on the road. Look at the first 40 vehicles that drive by. Take note of the number of vehicles that are cars (sedans). Use the data you collect to construct confidence interval estimates of the proportion of vehicles that are cars (rather than trucks, vans, etc). Report your confidence interval to the group. Why might people get different results? Is your sample likely a good representation of the total population of all vehicles? Why or why not?
Answer:
The confidence interval is ( 0.225952516, 0.474047484)
People will get different results because, the amount of sedans may be dependent on the area in which the data is taken.
No, the sample is not really a good representation of the whole population of vehicles, since only a certain area was sampled or experimented.
Step-by-step explanation:
Solution
Given that:
From the experiment we discovered that out of 40 vehicles, 14 of them were sedans.
Let us note that:
p^ = It is the point estimate of the population proportion
Where,
n=/n = 0.35
We also check for the standard error of p, sp:
which is,
sp =√{p^ (1-p^)/n] =0.075415516
Thus,
for the the critical z, we have the following:
α/2 = 0.05
So,
z (α)/2 = 1.644853627
Thus,
For lower bound = p^ - z(α/2) * sp = 0.225952516
For upper bound = p^ + z(α/2)* sp = 0.474047484
Hence,
The confidence interval becomes: ( 0.225952516, 0.474047484)
