Answer:
(a) The 95% confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is (0.34, 0.40).
(b) Not reasonable.
Step-by-step explanation:
The information provided is:
n = 1000
[tex]\hat p[/tex] = 0.37
(a)
The (1 - α)% confidence interval for the population proportion p is:
[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
Here,
[tex]\hat p[/tex] = sample proportion
n = sample size
[tex]z_{\alpha/2}[/tex] = critical value of z.
Compute the critical value of z for 95% confidence interval as follows:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]
*Use a z-table for the value.
Compute the 95% confidence interval for the population proportion p as follows:
[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]=0.37\pm 1.96\times\sqrt{\frac{0.37(1-0.37)}{1000}}[/tex]
[tex]=0.37\pm 0.03\\=(0.34, 0.40)[/tex]
Thus, the 95% confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is (0.34, 0.40).
(b)
Now we need to determine whether it is reasonable to believe that the actual percent of people in the United States whose favorite sport to watch on television is American football is 33%.
The hypothesis can be defined as:
H₀: The percentage of people in the United States whose favorite sport to watch on television is American football is 33%, i.e. p = 0.33.
Hₐ: The percentage of people in the United States whose favorite sport to watch on television is American football is different from 33%, i.e. p ≠ 0.33
The hypothesis can be tested based on a confidence interval.
The decision rule:
If the (1 - α)% confidence interval includes the null value of the test then the null hypothesis will not be rejected. And if the (1 - α)% confidence interval includes the null value of the test then the null hypothesis will be rejected.
The 95 confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is (0.34, 0.40).
The confidence interval does includes the null value of p, i.e. 0.33.
So, the null hypothesis will be rejected.
Hence, concluding that is is not reasonable to believe that 33% is the actual percent of people in the United States whose favorite sport to watch on television is American football.
95% confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is (0.34, 0.40).
Concluding that is is not reasonable to believe that 33% is the actual percent of people in the United States whose favorite sport to watch on television is American football
Given that,
A recent survey collected information on television viewing habits from a random sample of 1,000 people in the United States.
Of those sampled, 37 percent indicated that their favorite sport to watch on television was American football.
We have to determine,
Construct and interpret a 95 percent confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football.
According to the question,
Sample proportion p = 37% = 0.37
Sample space n = 1000
The (1 - α)% confidence interval for the population proportion,[tex]C.I. = P \pm Z_\frac{\alpha}{2} \sqrt{\dfrac{p(1-p)}{n} }[/tex]
To compute the critical value of z for 95% confidence interval as follows:
[tex]z_\frac{ \alpha}{2} = z_\frac{0.05}{2} = 1.96[/tex]
By using a z-table for the value.
Compute the 95% confidence interval for the population proportion p as follows:
[tex]C.I. = p\pm Z_\frac{\alpha}{2} \sqrt{\dfrac{p(1-p)}{n} }\\\\C.I. = 0.37\pm 1.96 \sqrt{\dfrac{0.43(1-0.34)}{1000} }\\\\C.I.= 0.03 \pm 0.09\\\\C.I. = (0.34, \ 0.40)[/tex]
Hence, 95% confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is (0.34, 0.40).
The hypothesis can be defined as:H₀: The percentage of people in the United States whose favorite sport to watch on television is American football is 33%, i.e. p = 0.33.
Hₐ: The percentage of people in the United States whose favorite sport to watch on television is American football is different from 33%, i.e. p ≠ 0.33
The hypothesis can be tested based on a confidence interval.
The (1 - α)% confidence interval includes the null value of the test then the null hypothesis will not be rejected.
And if the (1 - α)% confidence interval includes the null value of the test then the null hypothesis will be rejected.
The 95 confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is (0.34, 0.40).
The confidence interval does includes the null value of p, i.e. 0.33.
So, the null hypothesis will be rejected.
Hence, Concluding that is is not reasonable to believe that 33% is the actual percent of people in the United States whose favorite sport to watch on television is American football
To know more about Probability click the link given below.
https://brainly.com/question/15694157
ktoś mi to rozwiarze pls
a)
[tex]2a+(3a-7)=2a+3a-7=5a-7[/tex]
b)
[tex](2x-3)+x=2x-3+x=3x-3[/tex]
c)
[tex]7-(5x+4)=7-5x-4=3-5x[/tex]
d)
[tex]3x-(y-2x)=3x-y+2x=5x-y[/tex]
e)
[tex]-(3a+6)-4=-3a-6-4=-3a-10[/tex]
f)
[tex]-(x-2y)-3x=-x+2y-3x=2y-4x[/tex]
g)
[tex](2p-1)+(3+5p)=2p-1+3+5p=7p+2[/tex]
h)
[tex](4-2x)-(7x-2)=4-2x-7x+2=6-9x[/tex]
i)
[tex]-(2x-1)+(3x+1)=-2x+1+3x+1=x+2[/tex]
j)
[tex](2m+4n)+(m-0,5n)=2m+4n+m-0,5n=3m+3,5n[/tex]
k)
[tex](4a-7b)-(2a+3b)=4a-7b-2a-3b=2a-10b[/tex]
l)
[tex]-(2p-r)-(2r-p)=-2p+r-2r+p=-p-r[/tex]
A 95% confidence interval was computed using a sample of 16 lithium batteries, which had a sample mean life of 645 hours. The confidence interval was (628.5, 661.5) hours. Which of the following would produce a confidence interval that is wider than the one originally computed (assuming everything else remained the same)? Select ALL that are correct. Having a sample with a larger standard deviation. Using a 99% confidence level instead of 95%. Removing an outlier from the data. Using a 90% confidence level instead of 95%. Testing 10 batteries instead of 16. Testing 24 batteries instead of 16.
Answer:
Step-by-step explanation:
Hello!
The mean life of 16 lithium batteries was estimated with a 95% CI:
(628.5, 661.5) hours
Assuming that the variable "X: Duration time (life) of a lithium battery(hours)" has a normal distribution and the statistic used to estimate the population mean was s Student's t, the formula for the interval is:
[X[bar]±[tex]t_{n-1;1-\alpha /2}* \frac{S}{\sqrt{n} }[/tex]]
The amplitude of the interval is calculated as:
a= Upper bond - Lower bond
a= [X[bar]+[tex]t_{n-1;1-\alpha /2}* \frac{S}{\sqrt{n} }[/tex]] -[X[bar]-[tex]t_{n-1;1-\alpha /2}* \frac{S}{\sqrt{n} }[/tex]]
and the semiamplitude (d) is half the amplitude
d=(Upper bond - Lower bond)/2
d=([X[bar]+[tex]t_{n-1;1-\alpha /2}* \frac{S}{\sqrt{n} }[/tex]] -[X[bar]-[tex]t_{n-1;1-\alpha /2}* \frac{S}{\sqrt{n} }[/tex]] )/2
d= [tex]t_{n-1;1-\alpha /2}* \frac{S}{\sqrt{n} }[/tex]
The sample mean marks where the center of the calculated interval will be. The terms of the formula that affect the width or amplitude of the interval is the value of the statistic, the sample standard deviation and the sample size.
Using the semiamplitude of the interval I'll analyze each one of the posibilities to see wich one will result in an increase of its amplitude.
Original interval:
Amplitude: a= 661.5 - 628.5= 33
semiamplitude d=a/2= 33/2= 16.5
1) Having a sample with a larger standard deviation.
The standard deviation has a direct relationship with the semiamplitude of the interval, if you increase the standard deviation, it will increase the semiamplitude of the CI
↑d= [tex]t_{n-1;1-\alpha /2}[/tex] * ↑S/√n
2) Using a 99% confidence level instead of 95%.
d= [tex]t_{n_1;1-\alpha /2}[/tex] * S/√n
Increasing the confidence level increases the value of t you will use for the interval and therefore increases the semiamplitude:
95% ⇒ [tex]t_{15;0.975}= 2.131[/tex]
99% ⇒ [tex]t_{15;0.995}= 2.947[/tex]
The confidence level and the semiamplitude have a direct relationship:
↑d= ↑[tex]t_{n_1;1-\alpha /2}[/tex] * S/√n
3) Removing an outlier from the data.
Removing one outlier has two different effects:
1) the sample size is reduced in one (from 16 batteries to 15 batteries)
2) especially if the outlier is far away from the rest of the sample, the standard deviation will decrease when you take it out.
In this particular case, the modification of the standard deviation will have a higher impact in the semiamplitude of the interval than the modification of the sample size (just one unit change is negligible)
↓d= [tex]t_{n_1;1-\alpha /2}[/tex] * ↓S/√n
Since the standard deviation and the semiamplitude have a direct relationship, decreasing S will cause d to decrease.
4) Using a 90% confidence level instead of 95%.
↓d= ↓[tex]t_{n_1;1-\alpha /2}[/tex] * S/√n
Using a lower confidence level will decrease the value of t used to calculate the interval and thus decrease the semiamplitude.
5) Testing 10 batteries instead of 16. and 6) Testing 24 batteries instead of 16.
The sample size has an indirect relationship with the semiamplitude if the interval, meaning that if you increase n, the semiamplitude will decrease but if you decrease n then the semiamplitude will increase:
From 16 batteries to 10 batteries: ↑d= [tex]t_{n_1;1-\alpha /2}[/tex] * S/√↓n
From 16 batteries to 24 batteries: ↓d= [tex]t_{n_1;1-\alpha /2}[/tex] * S/√↑n
I hope this helps!
Suppose a random sample of size is selected from a population with . Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate). a. The population size is infinite (to 2 decimals). b. The population size is (to 2 decimals). c. The population size is (to 2 decimals). d. The population size is (to 2 decimals).
Answer:
A) σ_x' = 1.4142
B) σ_x' = 1.4135
C) σ_x' = 1.4073
D) σ_x' = 1.343
Step-by-step explanation:
We are given;
σ = 10
n = 50
A) when size is infinite, the standard deviation of the sample mean is given by the formula;
σ_x' = σ/√n
Thus,
σ_x' = 10/√50
σ_x' = 1.4142
B) size is given, thus, the standard deviation of the sample mean is given by the formula;
σ_x' = (σ/√n)√((N - n)/(N - 1))
Thus, with size of N = 50,000, we have;
σ_x' = 1.4142 x √((50000 - 50)/(50000 - 1))
σ_x' = 1.4142 x 0.9995
σ_x' = 1.4135
C) at N = 5000;
σ_x' = 1.4142 x √((5000 - 50)/(5000 - 1))
σ_x' = 1.4073
D) at N = 500;
σ_x' = 1.4142 x √((500 - 50)/(500 - 1))
σ_x' = 1.343
The value of the standard error in each of the following are:
A) σ_x' = 1.4142
B) σ_x' = 1.4135
C) σ_x' = 1.4073
D) σ_x' = 1.343
Standard error calculation:Given:
σ = 10
n = 50
A) when size is infinite, the standard deviation of the sample mean is given by the formula;
σ_x' = σ/√n
Thus,
σ_x' = 10/√50
σ_x' = 1.4142
B) size is given, thus, the standard deviation of the sample mean is given by the formula;
σ_x' = (σ/√n)√((N - n)/(N - 1))
Thus, with size of N = 50,000, we have;
σ_x' = 1.4142 x √((50000 - 50)/(50000 - 1))
σ_x' = 1.4142 x 0.9995
σ_x' = 1.4135
C) at N = 5000;
σ_x' = 1.4142 x √((5000 - 50)/(5000 - 1))
σ_x' = 1.4073
D) at N = 500;
σ_x' = 1.4142 x √((500 - 50)/(500 - 1))
σ_x' = 1.343
Find more information about Standard errors here:
brainly.com/question/1191244
Given f(x) and g(x) = f(x + k), use the graph to determine the value of k. Two lines labeled f of x and g of x. Line f of x passes through points negative 4, 0 and negative 2, 2. Line g of x passes through points negative 10, 0 and negative 8, 2.
Answer:
Sorry about that answer, some people are plain rude, but the correct answer is -5.
Step-by-step explanation:
Hope this Helps! Good Luck!
Answer: k=-5 is correct because if you were to divide -10/-2 it would give you -5
I hope this simplifies your question for the answer.
A particular project network has two paths through it: Path A and Path B. Path A has an expected completion time of 15 weeks and a variance in completion time of 8 weeks, while Path B has an expected completion time of 16 weeks and a variance in completion time of 4 weeks. What is the probability that this project is going to take more than 18 weeks?
Answer:
Probability that this project is going to take more than 18 weeks = 0.99991
Step-by-step explanation:
When independent distributions are combined, the combined mean and combined variance are given through the relation
Combined mean = Σ λᵢμᵢ
(summing all of the distributions in the manner that they are combined)
Combined variance = Σ λᵢ²σᵢ²
(summing all of the distributions in the manner that they are combined)
For this distribution, the total time the project will take = A + B
A ~ (15, 8)
B ~ (16, 4)
Combined mean = μ₁ + μ₂ = 15 + 16 = 31
Combined variance = 1²σ₁² + 1²σ₂² = 8 + 4 = 12
Combined Standard Deviation = √(12) = 3.464 weeks
So, with the right assumption that this combined distribution is a normal distribution
Probability that this project is going to take more than 18 weeks
P(x > 18)
We first normalize/standardize 18
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (18 - 31)/3.464 = - 3.75
The required probability
P(x > 18) = P(z > -3.75)
We'll use data from the normal probability table for these probabilities
P(x > 18) = P(z > -3.75) = 1 - P(x ≤ -3.75)
= 1 - 0.00009 = 0.99991
Hope this Helps!!!
The diagonal of a square has length 10√2. Find the area of the square.
Answer: [tex]A = 100[/tex] square unit
Step-by-step explanation:
The formula for calculating the area of a square when the diagonal is given is :
[tex]Area = d^{2} / 2[/tex]
That is :
[tex]A = \frac{(10\sqrt{2})^{2}}{2}[/tex]
[tex]A = \frac{100(2)}{2}[/tex]
[tex]A = 100[/tex] square unit
which of the following radical expressions is equivalent to....
Answer:
:=?¿ZV16
Step-by-step explanation:
If ax + y=23, 3x - y = 9, and x =8, what is the value of a ?
Answer:
a = 1
Step-by-step explanation:
x = 8
3x - y = 9
3(8) - y = 9
24 - y = 9
-y = 9 - 24
-y = -15
y = 15
ax + y = 23
a(8) + 15 = 23
8a = 23 - 15
8a = 8
a = 8/8
a = 1
The sum of number times 3 and 15
Answer:
3x+15
Step-by-step explanation:
When it says "the sum of a number three times", it means 3x, because the x stands for multiplication and the problem says the sum sum is between 3x and the number 15. So your equation is 3x+15. Hope this helps ;)
You are doing marketing research about yogurt consumption. Based on your previous research, you feel sure that the population standard deviation of the number of yogurts consumed per year is 6. In other words, σ is known and σ = 6. You take a sample of 50 consumers and the sample mean is 32 yogurts consumed per year. In other words, = 32. You want to develop a confidence interval for μ푥(the population mean) such that you are 90% confident that the true value of μ lies within the interval.1. What is the value of ?훼
Answer:
Step-by-step explanation:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Since the sample size is large and the population standard deviation is known, we would use the following formula and determine the z score from the normal distribution table.
Margin of error = z × σ/√n
Where
σ = population standard Deviation
n = number of samples
From the information given
1) x = 32
σ = 6
n = 50
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.90 = 0.1
α/2 = 0.1/2 = 0.05
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.05 = 0.95
The z score corresponding to the area on the z table is 1.645. Thus, confidence level of 90% is 1.645
Margin of error = 1.645 × 6/√50 = 1.4
Confidence interval = 32 ± 1.4
The lower end of the confidence interval is
32 - 1.4 = 30.6
The upper end of the confidence interval is
32 + 1.4 = 33.4
is 8 · 9 -5= 72-5 an expression?
Answer:no
Step-by-step explanation:
expressions don't have equal sides
so it's an equation
please like and Mark as brainliest
How do I work this problem-×+6×=10
Answer:
add -x to 6x to get 5x then divide by 5 to get 2 x is 2
Step-by-step explanation:hope this helps god bless
Step-by-step explanation:
I think you have to find value of x
-x + 6x = 10
5x = 10
x = 10 / 5 = 2
x = 2
The owner of Get-A-Away Travel has recently surveyed a random sample of 337 customers to determine whether the mean age of the agency's customers is over 20. The appropriate hypotheses are Upper H 0: muequals20, Upper H Subscript a Baseline : mu greater than 20. If he concludes the mean age is over 20 when it is not, he makes a __________ error. If he concludes the mean age is not over 20 when it is, he makes a __________ error.
Answer:
On this case we want to test if the mean age of the agency's customers is over 20, so the system of hypothesis would be:
Null hypothesis: [tex]\mu \leq 20[/tex]
Alternative hypothesis: [tex]\mu >20[/tex]
If he concludes the mean age is over 20 when it is not, he makes a type I error . If he concludes the mean age is not over 20 when it is, he makes a Type II error error.
Step-by-step explanation:
Previous concepts
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
Type I error, also known as a “false positive” is the error of rejecting a null hypothesis when it is actually true. Can be interpreted as the error of no reject an alternative hypothesis when the results can be attributed not to the reality.
Type II error, also known as a "false negative" is the error of not rejecting a null hypothesis when the alternative hypothesis is the true. Can be interpreted as the error of failing to accept an alternative hypothesis when we don't have enough statistical power.
Solution to the problem
On this case we want to test if the mean age of the agency's customers is over 20, so the system of hypothesis would be:
Null hypothesis: [tex]\mu \leq 20[/tex]
Alternative hypothesis: [tex]\mu >20[/tex]
If he concludes the mean age is over 20 when it is not, he makes a type I error . If he concludes the mean age is not over 20 when it is, he makes a Type II error error.
When the travel agency owner concludes the mean age is over 20 when it's not, it's called a Type I error. If he concludes it's not over 20 when it is, it is a Type II error.
The scenario described involves a hypothesis test concerning the mean age of customers at a travel agency. When the travel agency owner incorrectly concludes that the mean age is over 20 when in fact it is not, he is making a Type I error. Conversely, if he concludes that the mean age is not over 20 when it actually is, that would be a Type II error. Understanding the consequences of these errors is critical in statistics because they affect decision-making processes based on data analysis.
The distance between flaws on a long cable is exponentially distributed with mean 12 m.
a. Find the probability that the distance between two flaws is greater than 15m.
b. Find the probability that the distance between two flaws is between 8 and 20 m.
c. Find the median distance.
d. Find the standard deviation of the distances.
e. Find the 65th percentile of the distances.
The question asks for various measures of an exponentially distributed statistic, the distance between flaws on a cable. To find these, we use formulas specific to the exponential distribution; for example, the median is calculated as ln(2) * mean, and the standard deviation is equal to the mean, computed with the formula σ = √variance = √mean.
Explanation:The problem can be modeled using the exponential distribution in statistics. The exponential distribution is often used to model the time elapsed between events in a Poisson point process, or in our case, the distance between the flaws in the cable.
The probability that the distance between two flaws is greater than 15m can be calculated using the formula:https://brainly.com/question/37170119
#SPJ3
In this problem, we're calculating properties of an exponential distribution representing the distances between flaws in a cable. The probability that a given distance is more than 15m is 22.31%, and between 8m and 20m is 48.57%. The median distance is around 8.317m, the standard deviation is 12m, and the 65th percentile is about 14.791m.
Explanation:In this problem, the distance between flaws on a long cable is exponentially distributed with a mean of 12 m. That means the lambda (λ) parameter's rate of occurring flaws per meter is 1/mean, or approximately 0.0833.
For a given exponential distribution, the probability that a random variable X is greater than x is given by P(X > x) = e^(-λx). So, to find the probability that the distance between flaws is greater than 15 m, we substitute 15 for x to get P(X > 15) = e^(-0.0833 * 15) approximately equals 0.2231 or 22.31%. The probability that the distance between two flaws is between 8 and 20 m will be P(8 < X < 20) = P(X < 20) - P(X < 8) which equates to (1 - e^(-0.0833 * 20)) - (1 - e^(-0.0833 * 8)). This calculates to approximately 0.4857 or 48.57%. From the properties of the exponential distribution, the median distance can be calculated using the formula ln2/λ, so the median is approximately 8.317 m. The standard deviation of an exponential distribution is the reciprocal of λ, which is simply the mean (μ). So the standard deviation is also 12 m. The 65th percentile of an exponential distribution can be calculated using the formula: -ln(1 - p) / λ where p is the percentile in decimal form. So the 65th percentile is -ln(1 - 0.65) / 0.0833 ≈ 14.791 m. Learn more about Exponential Distribution here:https://brainly.com/question/33722848
#SPJ2
Identify the value for the variable.
What is the value of x in this simplified expression?
7-9 · 7-3 = 7x
x =
What is the value of y in this simplified expression?
StartFraction 11 Superscript negative 4 Baseline Over 11 Superscript negative 8 Baseline EndFraction = 11 Superscript y
y =
Answer:
x= -12 y= 4
Step-by-step explanation:
Answer:
Y=4
x=-12
Step-by-step explanation:
Find the circumference of the circle with the given radius. Round to the nearest tenth. Use 3.14 for π.
r = 8 cm
Step-by-step explanation:
Circumference of the circle= 2πr
=2×3.14×8 cm
= 50.24cm
= 50.2 cm
Answer:
50.27
rounded : 50.3
Step-by-step explanation:
2 times 3.14 times 8
hope this helped
brainliest is appreciated :)
A citrus farmer who grows mandarin oranges finds that the diameters of mandarin oranges harvested on their farm follow a normal distribution with a mean of 5.85 cm and a standard deviation of 0.24 cm. Find the probability that a randomly selected mandarin orange from this farm has a diameter larger than 6.0 cm. Enter your probability as a decimal value rounded to 3 decimal places.
Answer:
0.266
Step-by-step explanation:
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.
In this problem, we have that:
[tex]\mu = 5.85, \sigma = 0.24[/tex]
Find the probability that a randomly selected mandarin orange from this farm has a diameter larger than 6.0 cm.
This is 1 subtracted by the pvalue of Z when X = 6.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{6 - 5.85}{0.24}[/tex]
[tex]Z = 0.625[/tex]
[tex]Z = 0.625[/tex] has a pvalue of 0.734
1 - 0.734 = 0.266
Answer:
[tex]P(X>6)=P(\frac{X-\mu}{\sigma}>\frac{6-\mu}{\sigma})=P(Z>\frac{6-5.85}{0.24})=P(z>0.625)[/tex]
And we can find this probability using the complement rule and the normal standard table or excel:
[tex]P(z>0.625)=1-P(z<0.625)=1-0.734= 0.266[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the diameters of mandarin oranges of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(5.85,0.24)[/tex]
Where [tex]\mu=5.85[/tex] and [tex]\sigma=0.24[/tex]
We are interested on this probability
[tex]P(X>6)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(X>6)=P(\frac{X-\mu}{\sigma}>\frac{6-\mu}{\sigma})=P(Z>\frac{6-5.85}{0.24})=P(z>0.625)[/tex]
And we can find this probability using the complement rule and the normal standard table or excel:
[tex]P(z>0.625)=1-P(z<0.625)=1-0.734= 0.266[/tex]
A person measures the contents of 25 pop cans and finds the mean content to be 12.1 fluid ounces with a standard deviation of 0.2 ounces. Construct a 99% confidence interval for the average fluid content of a can.
Answer:
The 99% confidence interval for the average fluid content of a can is between 11.54 and 12.66 fluid ounces.
Step-by-step explanation:
We are in posession of the sample's standard deviation, so we use the student 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 = 25 - 1 = 24
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995([tex]t_{995}[/tex]). So we have T = 2.797
The margin of error is:
M = T*s = 2.797*0.2 = 0.56
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 12.1 - 0.56 = 11.54 fluid ounces.
The upper end of the interval is the sample mean added to M. So it is 12.1 + 0.56 = 12.66 fluid ounces.
The 99% confidence interval for the average fluid content of a can is between 11.54 and 12.66 fluid ounces.
Integrated circuits consist of electric channels that are etched onto silicon wafers. A certain proportion of circuits are defective because of "undercutting," which occurs when too much material is etched away so that the channels, which consist of the unetched portions of the wafers, are too narrow. A redesigned process, involving lower pressure in the etching chamber, is being investigated. The goal is to reduce the rate of undercutting to less than 5%. Out of the first 1000 circuits manufactured by the new process, only 35 show evidence of undercutting. Can you conclude that the goal has been met? Find the P-value and state a conclusion.
Answer:
There is statistical evidence to support the claim that the goal of reducing the rate of undercutting to less than 5% has been met.
P-value=0.01923.
Step-by-step explanation:
We have to test the hypothesis that the proportion of defective circuits is under 5%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.05\\\\H_a:\pi<0.05[/tex]
We will assume a level of significance of 0.05.
The sample, of size n=1000, has 35 defecteive circuits, so the sample proportion is:
[tex]p=35/1000=0.035[/tex]
The standard error is calculated as if the null hypothesis is true, so it is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.05*0.95}{1000}}}=\sqrt{0.0000475}=0.007[/tex]
The z-statistic can be calculated as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.035-0.050+0.5/1000}{0.007}=\dfrac{-0.0145}{0.007}= -2.07[/tex]
For this one-tailed test, the P-value is:
[tex]P-value=P(z<-2.07)=0.01923[/tex]
As the P-value is smaller than the significance level, the effect is significant and the null hypothesis is rejected. There is statistical evidence to support the claim that the goal of reducing the rate of undercutting to less than 5% has been met.
2. Find the Area of the triangle.
as do
12 yd
15 yd
Given:
The base of the triangle = 15 yd
The height of the circle = 12 yd
To find the area of the triangle.
Formula
The area of the triangle is
[tex]A=\frac{1}{2} bh[/tex]
where, b be the base of the triangle
h be the height of the triangle
Now,
Putting, b= 15 and h=12 we get,
[tex]A=\frac{1}{2} (15)(12)[/tex] sq yd
or, [tex]A = 90[/tex] sq yd
Hence,
The area of the triangle is 90 sq yd.
Answer:
A =90 yd^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh
A = 1/2(15)*12
A =90 yd^2
Law firm averages 149 cases per year with a standard deviation of 14 points. Suppose the law firm's cases per year are normally distributed. Let X= the number of cases per year. Then X∼N(149,14). Round your answers to THREE decimal places.
Answer: the z- score when x= 186 is 2.643
the mean is 149
this z score tells you that x= 186 is 2.643 standard dev. to the right of the mean
Figure ABCD is a parallelogram.
What are the lengths of line segments AB and BC?
3
-2
в
• AB = 4, BC = 16
AB = 4; BC = 8
AB = 10; BC = 20
• AB = 10; BC = 28
y
+
6
Given:
Given that ABCD is a parallelogram.
The length of AB is 3y - 2.
The length of BC is x + 12.
The length of CD is y + 6.
The length of AD is 2x - 4.
We need to determine the length of AB and BC.
Value of y:
We know the property that opposite sides of a parallelogram are congruent, then, we have;
[tex]AB=CD[/tex]
Substituting the values, we get;
[tex]3y-2=y+6[/tex]
[tex]2y-2=6[/tex]
[tex]2y=8[/tex]
[tex]y=4[/tex]
Thus, the value of y is 4.
Value of x:
We know the property that opposite sides of a parallelogram are congruent, then, we have;
[tex]AD=BC[/tex]
Substituting the values, we get;
[tex]2x-4=x+12[/tex]
[tex]x-4=12[/tex]
[tex]x=16[/tex]
Thus, the value of x is 16.
Length of AB:
The length of AB can be determined by substituting the value of y in the expression 3y - 2.
Thus, we have;
[tex]AB=3(4)-2[/tex]
[tex]=12-2[/tex]
[tex]AB=10[/tex]
Thus, the length of AB is 10 units.
Length of BC:
The length of BC can be determined by substituting the value of x in the expression x + 12.
Thus, we have;
[tex]BC=16+12[/tex]
[tex]BC=28[/tex]
Thus, the length of BC is 28 units.
Hence, the length of AB and BC are 10 units and 28 units respectively.
Find a6: 1, 1/2, 1/6, 1/24, 1/120, a6, 1/5,040, ...
Answer:
Is the #6 in the row. Is this a riddle
Answer:
its 1/720 i just took it
Step-by-step explanation:
You and a friend are selling lemonade. You sell three times as many cups as your friend. What percent of the cups sold were sold by your friend? Explain.
Answer:
Step-by-step explanation:
Friend sells x cups
You sell 3x cups
Total cups sold:: 4x
Ans: x/4x = 1/4 = 25%
Final answer:
The fraction of cups sold by your friend is x/4x, which gives us 25% of the total sales when converted to a percentage.
Explanation:
To find out what percent of the cups sold were sold by your friend, we can set up a simple ratio.
Let's assume your friend sold x cups.
According to the problem, you sold three times as many cups, so you sold 3x cups.
The total number of cups sold is the sum of the cups you both sold, which is x + 3x = 4x cups.
Now, we want to find out what fraction of the total sales x represents.
Since your friend sold x cups out of the total 4x, the fraction is x/4x.
To convert this fraction to a percentage, we multiply it by 100%.
Therefore, the percentage of cups sold by your friend is (x/4x) × 100% = 25%.
This calculation shows that your friend sold 25% of the cups.
An experienced ice skater spins on the ice, creating a perfect circle with a diameter of 8 feet. What is the circles radius?
Answer:
radius-4
Step-by-step explanation:
the radius is half of the diameter
The SAT and ACT college entrance exams are taken by thousands of students each year. The mathematics portions of each of these exams produce scores that are approximately normally distributed. In recent years, SAT mathematics exam scores have averaged 480 with standard deviation 100. The average and standard deviation for ACT mathematics scores are 18 and 6, respectively. (a) An engineering school sets 555 as the minimum SAT math score for new students. What percentage of students will score below 555 in a typical year? (Round your answer to two decimal places.)
Answer:
77.34% of students will score below 555 in a typical year
Step-by-step explanation:
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.
SAT:
[tex]\mu = 480, \sigma = 100[/tex]
(a) An engineering school sets 555 as the minimum SAT math score for new students. What percentage of students will score below 555 in a typical year?
This is the pvalue of Z when X = 555. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{555 - 480}{100}[/tex]
[tex]Z = 0.75[/tex]
[tex]Z = 0.75[/tex] has a pvalue of 0.7734.
77.34% of students will score below 555 in a typical year
Find the surface area of a cylinder Give your answer in pi
It has a radius of 5 in and the height of 13 in
Answer:
565.2 in²
Step-by-step explanation:
2pi × r × (r + h)
2 × 3.14 × 5 × (5 + 13)
31.4 × 18
565.2
Solutes in the bloodstream enter cells through osmosis, which is the diffusion of fluid through a semipermeable membrane. Let C = C(t) be the concentration of a certain solute inside a particular cell. The rate at which the concentration inside the cell is changing is proportional to the difference in the concentration of the solute in the bloodstream and the concentration within the cell. Let k be the constant of proportionality. Suppose the concentration of a solute in the bloodstream is maintained at a constant level of L gm/cubic cm. Find the differential equation that best models this situation. (Use C for the concentration within the cell, not C(t).)
Answer:
since the rate at which concentration inside the cell is proportional to the difference in the concentration of the solute in the blood stream and the concentration within the cell, then the rate of change of concentration within the cell is equals to K(L-C).
Thus, the required differential equation is Δc/Δt = K( L - C ).
Step-by-step explanation:
The differential equation that models solute diffusion in osmosis is dC/dt = k*(L - C), representing the idea that the rate of change of the solute's concentration within the cell is proportional to the difference between the external and internal concentrations.
The differential equation that models this situation based on osmosis is expressed as dC/dt = k*(L - C), where C is the concentration of a solute within the cell, L is the constant level concentration in the bloodstream, and k is the constant of proportionality.
This equation is a simple expression of the rate of change being proportional to the difference between the outside and inside concentration levels. In this case, the rate of change of the concentration of solutes, dC/dt, is proportional to the difference between the concentration outside the cell, L, and the concentration inside the cell, C. The constant of proportionality is k.
This differential equation is a first order linear differential equation and represents processes that occur widely in nature, including in the diffusion of solutes through membranes in osmosis.
Learn more about Differential Equation here:
https://brainly.com/question/28052300
#SPJ6
What is the difference of the means of the distributions? 15 30 45 60
Answer:
The difference is 15.
Step-by-step explanation:
30-15=15
45-30=15
60-45=15
Answer:
I agree the difference is 15.
Step-by-step explanation:
State the conclusion based on the results of the test. The standard deviation standard deviation in in the pressure required to open a certain valve is known to be sigma equals 1.1 psi. σ=1.1 psi. Due to changes in the manufacturing process, the quality-control manager feels that the pressure pressure variability variability has changed changed. The null hypothesis was not rejected not rejected. Choose the correct answer below. A. There is is sufficient evidence that the standard deviation standard deviation in in the pressure required to open a certain valve has changed changed. B. There is is sufficient evidence that the standard deviation standard deviation in in the pressure required to open a certain valve has not changed. C. The standard deviation standard deviation in in the pressure has not changed. D. There is not is not sufficient evidence that the standard deviation standard deviation in in the pressure required to open a certain valve has not changed. E. There is not is not sufficient evidence that the standard deviation standard deviation in in the pressure required to open a certain valve has changed changed. F. The standard deviation standard deviation in in the pressure has changed changed.
Answer:
B
Step-by-step explanation:
Null hypothesis is not rejected if the test statistics show that the difference between observed and expected value is not significant and any difference is only due to chance.
So there is sufficient evidence from statistics that null hypothesis is true and the standard deviation in the pressure required to open a certain valve has not changed.
since evidence has to be there when null hypothesis is tested, optionC, D and E are rejected.
There is no change in standard deviation so option A and F are rejected.