Answer:
The width or range of the confidence interval with sample size 200 will be about half of that of the confidence interval with sample 50.
Step-by-step explanation:
Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)
- For the two random samples, of sizes 50 and 200, the Central limit theorem allows us to say that the sample mean is approximately equal to the population mean as this random sample satisfies the condition of being a simple random sample and a distribution obtained from a normal distribution.
- Making the right assumption that population standard deviation is known and z-distribution is used to find the critical value
Critical value for 95% = 1.96
The critical value for both samples are the same then.
- Standard Error of the mean = σₓ = (σ/√n)
where σ = population standard deviation
n = sample size
For the two distributions
Confidence Interval = (Sample mean) ± [(Critical value) × (Standard Error of the mean)
(Sample mean)₅₀ = (Sample mean)₂₀₀
(Critical value)₅₀ = (Critical value)₂₀₀
(Standard Error of the mean)₅₀ = (σ/√50) = 0.1414σ
(Standard Error of the mean)₂₀₀ = (σ/√200) = 0.0707σ
0.1414σ = 2 × 0.0707σ
(Standard Error of the mean)₅₀ = 2 × (Standard Error of the mean)₂₀₀
(Standard Error of the mean)₅₀ > (Standard Error of the mean)₂₀₀
Hence,
(Margin of Error)₅₀ > (Margin of Error)₂₀₀
(Margin of Error)₅₀ = 2 × (Margin of Error)₂₀₀
Confidence Interval = (Sample mean) ± (Margin of error)
Hence, the width or range of the confidence interval with sample size 50 will be about two times larger than the confidence interval with sample 200.
Hope this Helps!!!
A company estimates that 0.8% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $400. If they offer a 2 year extended warranty for $27, what is the company's expected value of each warranty sold?
Answer:
The expected value of each warranty sold is $23.8.
Step-by-step explanation:
0.8% probability of the product failling.
If the product fails, the company will lose 400 - 27 = $373. So a net value of -373.
100 - 0.8 = 99.2% probability of the product not failling.
If the product does not fail, the company gains $27.
What is the company's expected value of each warranty sold?
We multiply each outcome by its probability.
0.008*(-373) + 0.992*27 = 23.8
The expected value of each warranty sold is $23.8.
TIVITY MODULE
The length of a rectangle is eight centimeter less than
twice the width. The area of the rectangle is 24
centimeters squared. Determine the dimensions of the
rectangle in centimeters.
Answer: Length: 4, width: 6
Step-by-step explanation:
Let the length be x and width be y
Then x=2y-8 and xy=24
Substitute to get 2y-8 * y = 24, so 2y^2-8y=24 or y^2-4y=12, then solve to get y=6 or y=-2. Since width is positive y=6.
Substitute y=6 into xy=24 to get x=4.
Length: 4, width: 6
Hope that helped,
-sirswagger21
Bob is a travel agent. He receives 7% commission when he books a cruise for a customer. How much commission will he receive for booking a $3,900 cruise?
Answer:
$273
Step-by-step explanation:
$3900= 100%
$39 = 1%
39(1%)*7= $273 (7%)
The commission will he received should be $273
Given that,
He receives 7% commission when he books a cruise for a customercalculation:= 7% of $3,900
= $273
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Dorothy Kaatz, a computer programmer, earns a regular hourly rate of
$15.25 and earns double that when she works overtime. Kaatz usually works
40 regular hours and 12 hours overtime while she's trying to update the
company's systems before the month's end. What is her straight-time pay?
What is her overtime pay? What is her total pay?
Answer:
$976
Step-by-step explanation:
Straight time pay= $15.25(hourly rate) × 40(hours worked)= $610
Overtime Rate = 15.25×2= $30.50
Overtime Pay= $30.5 × 12 (Hours worked overtime)= $366
Total Pay= Basic wage + Overtime Wage = $976
What’s the correct answer for this?
Answer:
C.
Step-by-step explanation:
Density = Mass / Volume
2.7 = 54 / V
V = 54 / 2.7
V = 20 cubic cm
Assume that 1100 births are randomly selected and exactly 556 of the births are girls. Use subjective judgment to determine whether the given outcome is unlikely, and also determine whether it is unusual in the sense that the result is far from what is typically expected.
Answer:
The sample proportion for the births that are girls is 0.505. It is slightly higher than the expected value of 0.5, but the right way to answer if it is an unusual proportion is by performing an hypothesis test.
The hypothesis test results in not enough evidence to claim that the outcome is unlikely. This sample result has a probability of 0.7627 of appearing by pure chance in a population with proportion p=0.5.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the proportion of girls birth differs significantly from the expected proportion (50%).
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.5\\\\H_a:\pi\neq 0.5[/tex]
The significance level is 0.05.
The sample has a size n=1100.
The sample proportion is p=0.505.
p=X/n=556/1100=0.505
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{1100}}\\\\\\ \sigma_p=\sqrt{0.000227}=0.015[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.505-0.5-0.5/1100}{0.015}=\dfrac{0.005}{0.015}=0.302[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=2\cdot P(z>0.302)=0.7627[/tex]
As the P-value (0.7627) is greater 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 the proportion of girls birth differs significantly from the expected proportion (50%).
Graph the line that represents this equation. 3x - 4y =8
Answer:
See attachment
Step-by-step explanation:
The solution is given in the image.
Which graph is the graph of the function?The graph of a feature f is the set of all factors in the plane of the form (x, f(x)). We can also outline the graph of f to be the graph of the equation y = f(x). So, the graph of a feature is a special case of the graph of an equation.
What does the axis of a graph constitute?An axis is a line to the aspect or backside of a graph; it's far labeled to give an explanation for the graph's meaning and the devices of measurement. The x-axis, the horizontal line at the lowest of a graph, may be labeled to present facts about what the graph represents.
Learn more about graphs here: brainly.com/question/4025726
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Find the constant of variation k for the direct variation 3x+5y=0
Answer:
-3/5
Step-by-step explanation:
3x+5y=0
Subtract 3x from each side
3x+5y-3x=0-3x
5y = -3x
Divide each side by 5
5y/5 = -3x/5
y = -3/5 x
A direct variation is y = kx
y = -3/5 x
The constant of variation is -3/5
math question is attached below
and show your work
Answer:
[tex]V = \frac13 \pi r^2 h[/tex]
117.81
Step-by-step explanation:
r is half the diameter so 2.5 cm
h is 18
fill in and get:
V = [tex]\frac13 \pi \cdot 6.25 \cdot 18 \approx 117.81 cm^3[/tex]
The first term in the sequence 5, 7, −7, ... is 5. Each even-numbered term is 2 more than the previous term and each odd-numbered term, after the first, is (−1) times the previous term. For example, the second term is 5+2 and the third term is (−1)×7. What is the 255th term of the sequence?
Answer:
Step-by-step explanation:
According to the condition, your terms are arranged as
5, 7 , -7 ,-5, 5, 7, -7, 5, -5,...................
So one loop will have 4 terms: 5, 7, -7. -5
Hence after 63 loops, the new loop has only 3 terms. That means the last loop will be 5, 7 ,-7. In other words, the 255th term will be -7
Solve the following equation for x.
|x/4+3|<6
Answer:
x<12
Step-by-step explanation:
subtract both sides by -3 because you need to isolate x. then you have x/4<3. now you need to get rid of the 4. so you do the opposite of division and multiply 4 by both sides so you get x<12
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
3.6
Step-by-step explanation:
d = sqrt(3^2+2^2) = sqrt(13) = 3.6
What are the factors of 2x + 3x 54? Select two options
2x - 9
2x6
2x + 6
X-6
x+6
Answer:
(2x -9)(x +6)Step-by-step explanation:
Perhaps you're factoring ...
2x² +3x -54
= 2x² +12x -9x -54 . . . . rewrite 3x appropriately
= 2x(x +6) -9(x +6) . . . . factor pairs of terms
= (2x -9)(x +6) . . . . . . . . finish the factoring
The factors are (2x -9) and (x +6).
1. An LG Dishwasher, which costs $800, has a 20% chance of needing to be replaced in the first 2 years of purchase. A two-year extended warrantee costs $112.10 on a dishwasher. What is the expected value of the extended warranty assuming it is replaced in the first 2 years?
2. Approximately 10% of all people are left-handed. Consider a grouping of fifteen (15) people.
a. State the random variable.
b. Write the probability distribution.
c. Draw a histogram.
d. Describe the shape of the histogram.
e. Find the mean.
f. Find the variance.
g. Find the standard deviation.
Step-by-step explanation:
The expected value of the extended warrant is calculated as follow.
Value of Waranty
= 800 x 20% − 112.10
= 800 x 20/100 − 112.10
= 47.9
The expected value of the extended warranty assuming it is replaced in the first 2 years is given as follow.
Expected value=800-112.10=>687.90
Therefore, required expected value of extended warranty is 687.90
2.
Given information:
Number of Trials (n) = 15
Probability of Success (p) = 0.10
a) Let X represents the number of left-handed people.
b) The probability distribution follows binomial distribution.
X ∼ Binomial distribution
The probability distribution is given as follow.
P(X = x) = ^nCx(p)^x(1 − p)^n − x
c)The histogram is given as follow. (See attachment)
d) The shape of histogram is skewed right.
e) The mean is calculated as follow.
Mean
=n x p
= 15 x 0.10
= 1.5
f) The variance is calculated as follow.
Variance
= n x p x q
= 15 x 0.10 x 0.90
= 1.35
g) The standard deviation is calculated as follow.
Standard deviation
=√n x p x q
=√15 x 0.10 x 0.90
= 1.162
Is the function given by f(x)equalsleft brace Start 2 By 2 Matrix 1st Row 1st Column one fourth x plus 1 comma 2nd Column for x less than or equals 4 comma 2nd Row 1st Column 4 x minus 11 comma 2nd Column for x greater than 4 comma EndMatrix continuous at xequals4? Why or why not? Choose the correct answer below. A. The given function is continuous at xequals4 because ModifyingBelow lim With x right arrow 4 f (x )does not exist. B. The given function is not continuous at xequals4 because f(4) does not exist. C. The given function is continuous at xequals4 because the limit is 2. D. The given function is not continuous at xequals4 because ModifyingBelow lim With x right arrow 4 f (x )does not exist.
Answer:
C. The given function is continuous at x=4 because the limit is 2.
Step-by-step explanation:
Given the function:
[tex]f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right[/tex]
We are to determine if the function is continuous at x=4.
For a function to be continuous at some value c in its domain:
f(c) must be defined.[tex]Lim_{x \to c}$ f(x)[/tex] must exist. [tex]f(c)=Lim_{x \to c}$ f(x)[/tex]Now: at x=4
[tex]f(4)=\dfrac{1}{4}*4+1=2[/tex][tex]Lim_{x \to 4}f(x)=2[/tex]Since the two values are the same, we say that f(x) is continuous at x=4.
The correct option is C.
an amount was invested at r% per quarter. what value of r will ensure that accumulated amount at the end of one year is 1.5 times more than amount invested
Answer:
[tex]r=25.7\%[/tex] will ensure that accumulated amount at the end of one year is 1.5 times more than amount invested
Step-by-step explanation:
Given: An amount was invested at r% per quarter.
To find: value of r such that accumulated amount at the end of one year is 1.5 times more than amount invested
Solution:
Let P denotes amount invested and n denotes time
As an amount (A) was invested at r% per quarter,
[tex]A=P\left ( 1+\frac{r}{400} \right )^{4n}[/tex]
According to question, accumulated amount at the end of one year is 1.5 times more than amount invested.
So,
[tex]A=1.5P+P=2.5P\\A=2.5P\\P\left ( 1+\frac{r}{400} \right )^{4n}=2.5P[/tex]
Put n = 1
[tex]P\left ( 1+\frac{r}{400} \right )^{4}=2.5P\\\left ( 1+\frac{r}{400} \right )^{4}=2.5\\1+\frac{r}{400} =(2.5)^{\frac{1}{4}}\\\frac{r}{100}=(2.5)^{\frac{1}{4}}-1\\r=100\left [ (2.5)^{\frac{1}{4}}-1 \right ]\\=25.7\%[/tex]
A research company desires to know the mean consumption of meat per week among people over age 27. A sample of 1179 people over age 27 was drawn and the mean meat consumption was 1.5 pounds. Assume that the population standard deviation is known to be 1.2 pounds. Construct the 99% confidence interval for the mean consumption of meat among people over age 27. Round your answers to one decimal place.
Answer:
The 99% confidence interval for the mean consumption of meat among people over age 27 is between 1.4 pounds and 1.6 pounds.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575*\frac{1.2}{\sqrt{1179}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 1.5 - 0.1 = 1.4 pounds
The upper end of the interval is the sample mean added to M. So it is 1.5 + 0.1 = 1.6 pounds
The 99% confidence interval for the mean consumption of meat among people over age 27 is between 1.4 pounds and 1.6 pounds.
Accident rate data y1, ...., y12 were collected over 12 consecutive years t=1,2,...12. At over 12 consecutive years t = 1,2,..., 12. At the end of the 6th year, a change in safety regulations occured. FOr each of the following situations, set up a linear model of the form y=XB+E. Define X and B appropriately.
a. The accident rate y is a linear function of t with the new safety regulations having no effect.
b. The accident rate y is a quadratic function of t with the new regulations having no effect.
c. The accident rate y is a linear function of t. The slope for t>= 7 is the same as for t<7. However there is a discrete jump for t=7.
d. The accident rate y is a linear function of t. After t=7, the slope changes, with the two lines intersecting at t=7.
Answer:
The correct option is;
The accident rate is a linear model function of t. After t = 7, the slope changes, with the two lines intersecting at t = 7
Step-by-step explanation:
The given parameters are;
Accident rate data = y₁, y₂, y₃, y₄, y₅, y₆, y₇, y₈, y₉, y₁₀, y₁₁, y₁₂
Time at which data was recorded = t₁, t₂, t₃, t₄, t₅, t₆, t₇, t₈, t₉, t₁₀, t₁₁, t₁₂
Accident rate equation is a linear model given as follows;
y = X·B + E
Where:
y = Accident rate
X = Slope of linear model
B = Year
E = y intercept of model
At the end of the 6th year, a change in a regulation that affects safety, hence accident rate occurred given as follows;
Before the change in safety regulations occurred for year t < 7 y₁ = X₁B + E₁
After the change in safety regulations occurred for year t < 7 y₂ = X₂B + E₂
Therefore the slope changes from X₁ to X₂ after t = 7 with the second linear model starting from the end of the first linear model making the two lines intersect at t = 7 (the beginning of year 7)
Hence the correct option is that "The accident rate is a linear model function of t. After t = 7, the slope changes, with the two lines intersecting at t = 7."
What’s the correct answer for this question?
Answer:
C
Step-by-step explanation:
A cylinder is formed when rotating the 3-D figure around y-axis
An option to buy a stock is priced at $150. If the stock closes above 30 next Thursday, the option will be worth $1000. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30, the option will be worth $200. A trader thinks there is a 50% chance that the stock will close in the 20-30 range, a 20% chance that it will close above 30, and a 30% chance that it will fall below 20.
Required:
a. Create a valid probability table.
b. How much should the trader expect to gain or lose?
c. Should the trader buy the stock? Explain.
Answer:
Step-by-step explanation:
An option to buy a stock is priced at $150. If the stock closes above 30 next Thursday, the option will be worth $1000. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30, the option will be worth $200. A trader thinks there is a 50% chance that the stock will close in the 20-30 range, a 20% chance that it will close above 30, and a 30% chance that it will fall below 20.
a) Let X represent the price of the option
x P(X=x)
$1000 20/100 = 0.2
$200 50/100 = 0.5
$0 30/100 = 0.3
b) Expected option price
[tex]= \sum x.P(X=x)\\\\ = 1000 * 0.2 + 200 * 0.5 + 0 = \$ 300[/tex]
Therefore expected gain = $300 - $150 = $150
c) The trader should buy the stock. Since there is an positive expected gain($150) in trading that stock option.
What is the purchase price of the land
Answer:
Answer:B. $100,000
Step-by-step explanation:
x is the number of years since the purchase of the land.
That means that when 0 years have passed by, it is when the land was purchased.
At x = 0, the price of the land was $100,000.
That means that the purchase price of the land is $100,000.
1/x=1/2 / 4/5
Solve for x.
X =
Answer:
1/x = 1/2÷4/5
1/x=1/2 x 5/4
1/x=5/8
5x=8
x=1.6
A shop has 4 types of sweets (chocolate, taffy, gummies, and cookies), 2 types of snacks (chips and crackers), and 3 types of drinks (sodas, juice, and sports drinks).
Mystery boxes are put together that randomly combine 1 sweet, 1 snack, and 1 drink.
What is the probability that a mystery box contains chocolate, chips, and juice?
Answer:
1/24
Step-by-step explanation:
1/4*1/2*1/3 = 1/24
I need help with this one
Answer:
-12
Step-by-step explanation:
Question 1 of 20 :
Select the best answer for the question.
1. Divide7/15 by 3/5
OA%
O B./25
O c. 75/21
O D.21/75
Answer:
7/9
Step-by-step explanation:
7/15 ÷ 3/5
Copy dot flip
7/15 * 5/3
7/3 * 5/15
7/3 * 1/3
7/9
Electricity usage data consists of 45 months has a mean number of units consumed is 390.47 per month with a standard deviation of 170.5 units per month. Assume that the number of units consumed are approximately normally distributed. Estimate 95% confidence interval for the average monthly electricity consumed units.
Answer:
The 95% confidence interval for the average monthly electricity consumed units is between 47.07 and 733.87
Step-by-step explanation:
We have the standard deviation for the sample. So we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 45 - 1 = 44
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 44 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0141
The margin of error is:
M = T*s = 2.0141*170.5 = 343.4
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 390.47 - 343.40 = 47.07 units per month
The upper end of the interval is the sample mean added to M. So it is 390.47 + 343.40 = 733.87 units per month
The 95% confidence interval for the average monthly electricity consumed units is between 47.07 and 733.87
A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).The results of the regression were:
y = a + bx
a = -0.762
b = 0.119
r2 = 0.8649
r = 0.93
A) Write the equation of the Least Squares Regression line of the form y = + x
B) If a country increases its life expectancy, the happiness index will increase or decrease?
C) If the life expectancy is increased by 3.5 years in a certain country, how much will the happiness index change?
D) Use the regression line to predict the happiness index of a country with a life expectancy of 67 years.
Answer:
(A) [tex]y=-0.762+0.119x[/tex]
(B) If a country increases its life expectancy, the happiness index will increase.
(C) If the life expectancy is increased by 3.5 years in a certain country, the happiness index will increase by 0.4165.
(D) If the life expectancy is 67 years in a certain country, the happiness index will be 7.21.
Step-by-step explanation:
A regression analysis was performed to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).
The output of the regression analysis are as follows:
a = -0.762
b = 0.119
r² = 0.8649
r = 0.93
(A)
The equation of the Least Squares Regression line of the form y = _ + _ x is:
[tex]y=-0.762+0.119x[/tex]
(B)
The correction between the variables happiness index (y) and life expectancy in years of a given country (x) is, 0.93.
The correlation coefficient is positive. This implies that there is a positive relation between the two variables, i.e. as the value of life expectancy in years increases the happiness index also increases.
Thus, if a country increases its life expectancy, the happiness index will increase.
(C)
Compute the value of y for x = x + 3.5 as follows:
[tex]y=-0.762+0.119x[/tex]
[tex]=-0.762+0.119\times (x+3.5)\\\\=(-0.762+0.119x)+0.4165\\\\=y+0.4165[/tex]
Thus, if the life expectancy is increased by 3.5 years in a certain country, the happiness index will increase by 0.4165.
(D)
Compute the value of y for x = 67 as follows:
[tex]y=-0.762+0.119x[/tex]
[tex]=-0.762+0.119\times 67\\\\=-0.762+7.973\\\\=7.211\\\\\approx 7.21[/tex]
Thus, if the life expectancy is 67 years in a certain country, the happiness index will be 7.21.
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. (f + g)(x) = x - 7
Step-by-step explanation:
→Set it up, like so:
-3x - 5 + 4x - 2
→Add like terms (-3x and 4x, -5 and -2):
x - 7
What is the solution set up 7x^2+3X=0
Answer:
X=0,X=-3/7
Step-by-step explanation:
7x^2+3x=0
x(7x+3)=0
x=0
7x+3=0
7x=-3
x=-3/7.
Answer:-3/7
Step-by-step explanation:
Firstly add -3x to both sides of equation. 7x^2+3x-3x=0+-3x
7x^2=-3x
Divid both sides by X
7x^2/X=-3/X
7x=-3
Divid both sides by 7
7x/7=-3/7
X=-3/7
Simplify the quotient shown 3480 divided by 29
Answer:
120
Step-by-step explanation:
3480/29=120
120
Simplify ———
1
final result is 120
