Answer:
1/4
Step-by-step explanation:
9 divide by 18= 1/4
In 2008 the Better Business Bureau settled 75% of complaints they received (USA Today, March 2, 2009). Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is .75, the same as the overall proportion of complaints settled in 2008
a. Suppose you select a sample of 450 complaints involving new car dealers. Show the sampling distribution of .
b. Based upon a sample of 450 complaints, what is the probability that the sample proportion will be within .04 of the population proportion?
c. Suppose you select a sample of 200 complaints involving new car dealers. Show the sampling distribution of .
d. Based upon the smaller sample of only 200 complaints, what is the probability that the sample proportion will be within .04 of the population proportion?
e. As measured by the increase in probability, how much do you gain in precision by taking the larger sample in part (b)?
Answer:
Explained below.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
[tex]\mu_{\hat p}= p[/tex]
The standard deviation of this sampling distribution of sample proportion is:
[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]
(a)
The sample selected is of size n = 450 > 30.
Then according to the central limit theorem the sampling distribution of sample proportion is normally distributed.
The mean and standard deviation are:
[tex]\mu_{\hat p}=p=0.75\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.75(1-0.75)}{450}}=0.0204[/tex]
So, the sampling distribution of sample proportion is [tex]\hat p\sim N(0.75,0.0204^{2})[/tex].
(b)
Compute the probability that the sample proportion will be within 0.04 of the population proportion as follows:
[tex]P(p-0.04<\hat p<p+0.04)=P(\frac{-0.04}{0.0204}<\frac{\hat p-p}{\sigma_{\hat p}}<\frac{0.04}{0.0204})[/tex]
[tex]=P(-1.96<Z<196)\\=P(Z<1.96)-P(Z<-1.96)\\=0.975-0.025\\=0.95[/tex]
Thus, the probability that the sample proportion will be within 0.04 of the population proportion is 0.95.
(c)
The sample selected is of size n = 200 > 30.
Then according to the central limit theorem the sampling distribution of sample proportion is normally distributed.
The mean and standard deviation are:
[tex]\mu_{\hat p}=p=0.75\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.75(1-0.75)}{200}}=0.0306[/tex]
So, the sampling distribution of sample proportion is [tex]\hat p\sim N(0.75,0.0306^{2})[/tex].
(d)
Compute the probability that the sample proportion will be within 0.04 of the population proportion as follows:
[tex]P(p-0.04<\hat p<p+0.04)=P(\frac{-0.04}{0.0306}<\frac{\hat p-p}{\sigma_{\hat p}}<\frac{0.04}{0.0306})[/tex]
[tex]=P(-1.31<Z<196)\\=P(Z<1.31)-P(Z<-1.96)\\=0.9049-0.0951\\=0.8098\\\approx 0.81[/tex]
Thus, the probability that the sample proportion will be within 0.04 of the population proportion is 0.81.
(e)
The probability that the sample proportion will be within 0.04 of the population proportion if the sample size is 450 is 0.95.
And the probability that the sample proportion will be within 0.04 of the population proportion if the sample size is 200 is 0.81.
So, there is a gain in precision on increasing the sample size.
Omar made $144 for 12 hours of work.
At the same rate, how much would he make for 8 hours of work?
Please help
Answer:
96
Step-by-step explanation:
144/12= 12 ( each hour)
12( times) 8=96
Since they got 144 for 12 hours you have to divide the hours by the money to get the amount earned ever hour so you divide the total amount by the hour then use the information you got and then you multiply the amount of money by 8
What is the critical value for a chi-square test with 13 degrees of freedom at the 1 percent level of significance
Answer: 27.688
Step-by-step explanation:
The critical chi-square value [tex]\chi^2_{(df,\alpha)}[/tex] depends on significance level ([tex]\alpha[/tex]) and degrees of freedom (df) .
Given significance level: ([tex]\alpha[/tex]) = 1% = 0.01
Degrees of freedom (df)= 13
From the chi-square table, the critical chi-square value for df = 13 and [tex]\alpha =0.01[/tex]
is [tex]\chi^2_{(df,\alpha)}=27.688[/tex]
Hence, the required critical value = 27.688
Factorise fully
40-10g
Please do quick, will mark brainiest!!
Answer:
10(4-g)Step-by-step explanation:
[tex]40 - 10g[/tex]
Rewrite 40 as 4 × 10
[tex]4 \times 10 - 10g[/tex]
Factor out 10
[tex]10(4 - g)[/tex]
AsKevin Selma madelyn Louis
What is the measure of angle b?
Answer: 53
Step-by-step explanation: I just woke up I’m too tired to explain
What is the equation of a line that is perpendicular yo the line whose equation is 2y+3x=1?
Answer:
y = 2/3x + 1/2
Step-by-step explanation:
First, make the equation into a slope-intercept form:
2y + 3x = 1
2y = -3x + 1
y = -1.5x + 0.5
You can make it into a fraction:
y = -3/2x + 1/2
Now here's the equation:
y = 2/3x + 1/2
Hope this helps!
Let me know if I'm wrong :)
(01.06)
Rick is setting up a model train track that is
sono
feet long. No telephone pole is needed at the start of the track. However, along the track, he places a telephone
pole every
foot apart. How many telephone poles does he need? (Input number values only)
Numerical Answers Expected!
Answer for Blank 1
Answer:
2
Step-by-step explanation:
2
help please!!
For the following situation, identify the explanatory and response variable. Then discuss what reservations (think cautions) you might have about the results of the experiment. Asking “What if…” type questions may help.
Do the high, centered brake lights (which have been required on all U.S. cars since 1986) really reduce the frequency of rear-end collisions? Randomized comparative experiments with fleets of rental and business cars, done before the lights were required, showed that the third brake light reduced rear-end collisions by as much as 50%. After the lights were required the drop was only 5%.
The experiment is messed up. Business and rental drivers are usually much more careful in their driving patterns because the car isn't theirs. They are usually adults, experienced drivers who don't put themselves into risky driving situations. = Speeding, cutting off others etc.. It also didn't tell how much the cars were driven. There may have been a down turn in the economy and thus less business driving and same with the rentals. If they were used less after the installation then the study wasn't really valid. What was the price of gas before and after the instillation. Who did the study? Did the previous testers have any reason to skew the study? Did they own stock in the third light business? Was it the same people who did the study before who did the study afterwords? What was the average age of the drivers before and after? The study group may have aged and calmed down a bit more? What were the technology changes that occurred about the same time? Anti skid brakes, better material and tread designs for the tires, what about the design of the gages and their lighting. How about the window styles and size..larger windows mean better view and potentially less accidents. What were the safety aspects of the cars before compared to the cars after, were they the same makes and Models or did the rental and business learn that certain cars were safer than others and move to the safer Models? so many variables to consider but did the tester consider them all-probably not. Random studies study only a certain percentage of the total. Who's to say the second random study didn't get less experienced drivers to study? All good what ifs'.
Which is the smallest set of numbers
hahahaha wht? lol sry im stupid tbh
Which of the following is the correct factored form of the given equation?
4x 2 - 11x + 6 = 0
(2x + 3)(2x + 2) = 0
(2x - 3)(2x - 2) = 0
(4x - 3)(x - 2) = 0
Answer:
(4x - 3)(x-2) = 0
Step-by-step explanation:
4x² - 11x + 6 = 0
To factorize this equation,
-11
4x6
These numbers are the key to the solution:
find two numbers whose sum is -11 and the product is + 24 (4 x 6)
So, the numbers are -3 and -8
4x² - 8x - 3x + 6 = 0
4x(x -2) - 3(x - 2) = 0
(4x - 3)(x-2) = 0
Answer:
(4x - 3)(x - 2) = 0
That's your answer!!
Wendy and Mini earn $38 per week for delivering magazines. Wendy worked for x weeks and earned an additional total bonus of $15 Mini worked for y weeks. Which expression shows the total money, in dollars, that Wendy and Mini earned for delivering magazines
A: 53x + 38y
B: 38 + 15 + 38y
C: 38 - 15 + 38y
D: 38x + 53y
what is Pi? explain.
Answer:
Pi is a irrational number
Step-by-step explanation:
Pi is an irrational number because it never ends it keeps going on and one.
Pi is also 3.141592654.............. never ends
What is the distance from b (-35,25) to c (-20, 15)
Answer:
[tex]d = 5\sqrt{13}[/tex]
Step-by-step explanation:
Distance Formula: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Simply plug in the 2 coordinates into the distance formula to find distance d:
[tex]d = \sqrt{(-20-(-35))^2+(15-25)^2}[/tex]
[tex]d = \sqrt{(-20+35)^2+(-10)^2}[/tex]
[tex]d = \sqrt{(15)^2+100}[/tex]
[tex]d = \sqrt{225+100}[/tex]
[tex]d = \sqrt{325}[/tex]
[tex]d = 5\sqrt{13}[/tex]
Which of the following describes the transformation from figure 1 to figure 2 shown on the graph below
Answer:
(x+5, y-2)
Step-by-step explanation:
Move right 5 units and moves down 2 units
Suppose that the probability that a person books a hotel using an online travel website is 0.68. For the question that follows, consider a sample of fifteen randomly selected people who recently booked a hotel.
What is the probability that at least fourteen out of fifteen people used an online travel website when they booked their hotel? Round to three decimal places.
A.0.028
B.0.025
C.0.323
D.0.978
Answer:
the answer is d because 0.978 cool number like yaaaa.
Step-by-step explanation:
fun quashen first to answer correctly is getting 20 points ( usely you get 5 i am giving 20 ) do it correct and fast .
Answer:
the answer is D
Step-by-step explanation:
63+5(8+1/5)
the 6 and 3 is not 63 it is 6 and a 3 in the corner.
SAT scores: A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean mathematics SAT score to be 433 . Assume the population standard deviation is 115 .
(a) Construct a 99 % confidence interval for the mean mathematics SAT score for the entering freshman class. Round the answer to the nearest whole number.
Answer:
The 99% confidence interval is [tex] 403.33 < \mu < 462.67 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 100
The sample mean is [tex]\= x = 433[/tex]
The standard deviation is [tex]\sigma = 115[/tex]
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 2.58 * \frac{115 }{\sqrt{100} }[/tex]
=> [tex]E = 29.67 [/tex]
Generally 99% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex]433 -29.67 < \mu < 433 + 29.67[/tex]
=> [tex] 403.33 < \mu < 462.67 [/tex]
|-9×+7|+8 is less than or equal to 9
Answer:
I don’t think it’s neither less than it equal
Step-by-step explanation:
I could be wrong don’t listen to me :)
Two cars start traveling in the same direction around a circular road that is 80 km long. The speed of one car is 92 km/h and the sped of the other is 68 km/h. b How many minutes after the two cars start traveling will one car lap the other for the second time?
Answer:
200 minutes
Step-by-step explanation:
So we know that the speed is 92 km/h for the first car and 68 km/h for the second car. We do not know the time, but we do know that we need to convert it into minutes. The time for both cars would be x/60. Now we multiply speed by time and get distance. The first car would be 92 x/60 and the second would be 68 x/60, now we cross multiply and make an equation. 92x/60 - 68x/60 = 80, 24x = 80, x=200 minutes.
Write a multiplication expression using the following clues:
1. One factor is a two digit number between 1 and 10
2. One factor is a two digit number between 1 and 10 (different from the first)
3. The product is greater than 8, but less than 10
A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),}. Find the probability of getting two numbers whose sum is less than 10.
Write an equation of the line passing through the point (8, -5) that is parallel to the line 2x -6y = -3
Answer:
y=1/3x+10.5
Step-by-step explanation:
y=mx+b, the equation of the parallel line is y=1/3x+1/2. So we know the slope is 1/3 and all we need is the Y intercept (b). We can find that manually with arithmetic because we know the slope. It turns out to be 10.5
Is 8.253725372537 a irrational number
Answer:
no
Step-by-step explanation:
Pat earns $489 per week at her new job. Calculate her annual salary. (Do not enter $ or comma in your answer.)
Answer:
25,428 this was a peice of pie
Step-by-step explanation:
Linearize the data. Then find the least squares regression equation
Answer:
C
Step-by-step explanation:
How will you write 4x + 23y into a statement
Answer:
Tom wants to go to disneyland this weekend with 23 adults including himself and 4 children Ashley 3, Leslie 1, Brit 4, Victor 2. Children under the age of 6 pay "x" amount while anyone older pay "y" amount. What equation can tom use to find out how much the tickets in total will be.
Step-by-step explanation:
Y = Adults pay y amount - There are 23 adults
X =kids under 6 pay x amount - there are 4 children
4x+23y
4 (kids under 6 ticket cost)+ 23 (Adults ticket cost)
$5.97 / 2
please show your work! I'll give brainliest to whoever shows work.
Answer:
2.99
Step-by-step explanation:
1.) 2 goes into 5 2 times. So the 2 goes on top of the division sign
2.) 2x2=4
3.) Move 4 below 5
4.) Subtract 5-4=1
5.) Bring down 9
6.) 2 Goes into 19 9 times
7.) 2x9=18
8.) 19-18=1
9.) Bring down the 7
10.) 2 Goes into 17 8 times
11.) 2x8= 16
12.) 17-16=1
13.) Add a zero onto the end, bring down that zero
14.) 2 goes into 10 5 times.
15.) Round answer to 2.99 because with money you only have two decimals
two angles are complementary.the measure of the larger angle is two times the measure of the smaller angle .What is the measure of each angle ?
We know that :
The sum of two angles that are complementary = 90°
Smaller angle = x
Larger angle = 2x
We can make the formula as
= 2x + x = 90°
= 3x = 90°
= x = 90 ÷ 3
= x = 30
The smaller angle = x = 30°
The larger angle = 2x = 30 × 2 = 60°
Therefore , the measure of each of the angles are 30° and 60° .