Using the z-distribution, the 95% confidence interval for the proportion of critical strikes out of all attacks is given by:
0.3752 < p < 0.4542
What is a confidence interval of proportions?A confidence interval of proportions is given by the following rule:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the parameters are described as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The character has 248 critical strikes out of 598 attacks, hence the values of the parameters are given as follows:
[tex]n = 598, \pi = \frac{248}{598} = 0.4147[/tex]
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The lower bound of the interval is given as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4147 - 1.96\sqrt{\frac{0.4147(0.5853)}{598}} = 0.3752[/tex]
The upper bound of the interval is given as follows:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4147 + 1.96\sqrt{\frac{0.4147(0.5853)}{598}} = 0.4542[/tex]
What is the missing information?The problem asks for the 95% confidence interval for the proportion of critical strikes out of all attacks.
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The heights of the 430 National Basketball Association players were listed on team rosters at the start of the 2005–2006 season. The heights of basketball players have an approximate normal distribution with mean,
= 79 inches
and a standard deviation,
= 3.89 inches.
1. If an NBA player reported his height had a z-score of 3.4, would you believe him? Explain your answer. (Round your answer to two decimal places.)
A z-score of 3.4 equates to a height of ____
A z-score of 3.4 equates to a height of 92.23
How to solve for the z scoreWe have to find the height of the player given the figures that we have in he question
We have the formula for the height as
z = x - u / sd
where z is the z score of the player = 3.4
x is the average which is not given here. This would be the height
u is = mean which is the value of 79 inches
while the standard deviation is given by sd = 3.89
We have to put these values in the formula that we have here. Such that we would have
3.4 = x - 79 / 3.89
we have to cross multiply
3. 89 * 3.4 = x - 79
13.226 = x - 79
x = 79 + 13.226
x = 92.23
From the value that we have here, we can see that the height of the player that was reported is given as 92. 23.
This is not believable because it would mean that the height is far greater than the height of all of the players which is 79 inches.
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Log11= Log(x-2) + Log5
Answer:
x = 4.2
Explanation:
log 11 = log(x - 2) + log(5)
log 11 = log(5x - 10)
Taking antilog,
11 = 5x - 10
5x = 21
x = 4.2
There are 69 students in BIO 101 this term, which is 15% higher than the enrollment in the class last term. How many students were in the class last term?
In comparison to last year's class, this year there are [tex]15[/tex]‰ more students. That means there were [tex]60[/tex] students in the class.
Who are called as students?
Someone who is enrolled in school or another type of educational facility is called a student. A "student" is someone who attends secondary school or above in the United Kingdom and the majority of commonwealth nations; "pupils" are those who attend primary or elementary schools.
A student is a person who attends school in order to learn. In addition to being people who attend school, such as children, teenagers, or adults, students can also be those who are learning elsewhere, such as in a college or university. A younger student is frequently referred to as a pupil.
Required calculations are,
Let the number of students in last year's class be [tex]x[/tex].
Increase in number of students by [tex]15[/tex]% or [tex]0.15.[/tex]
This year’s strength is [tex]69[/tex].
[tex]1x + 0.15 x = 69[/tex]
[tex]1.15 x = 69\\x = 69/1.15\\x=60[/tex]
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it is actually "just ABOVE 30" and NOT below.
The median acceptance rate of the histogram is given as follows:
Just above 30%.
What is the median of a data-set?The median of a data-set is the middle value of the data-set, the value of which 50% of the measures in the data-set are less than and 50% are greater than.
To find the median of the given histogram, first we have to identity the number of measures in the histogram, adding the frequencies as follows:
number of frequencies = 1 + 3 + 5 + 3 + 5 + 5 + 1 + 2 = 25.
The cardinality is odd, of 25, hence the median is the interval of the histogram in which the cumulative frequency reaches 13.
Taking the midpoint of each interval, the cumulative frequencies are as follows:
12.5: 1.17.5: 1 + 2 = 3.22.5: 3 + 5 = 8.27.5: 8 + 3 = 11.32.5: 11 + 5 = 16 -> greater than 13, hence the median is of 32.5.32.5 is just above 30%, which is the correct option.
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PLEASE ANSWER ASAP
A random sample of n50 ASU students shows that they spend an average of $3.17 on coffee/tea each day with standard error of about $1.11. FIND and INTERPRET a 95% confidence interval for the mean amount spent on coffee/tea by an ASU student Note: you do not have to show work on how you found your interval, but you do need to be thorough with your interpretation of the found interval.
Answer:
so the ans is $10.43
I know I am not that smart
Explanation:
thank you
Information and knowledge: Which one is obtained from the other?
Answer:
Information is obtained from knowledge because you can utilize your current knowledge to learn new information.
what is a properly of matter give me 5 examples
Explanation:
Density, colour, hardness, melting and boiling points, and electrical conductivity are all examples of physical properties.
Consider the following two data sets. Data Set 1: 8 16 20 35 Data Set II: 5 13 17 32 Note that each value of the second data set is obtained by subtracting 3 from the corresponding value of the first data set. a. Calculate the mean for each of these two data sets. Comment on the relationship between the two means. b. Calculate the standard deviation for each of these two data sets. Comment on the relationship, between the two standard deviations.
1. The mean for each of these two data sets is 0.058.
2. The standard deviation for each of these two data sets is 0.465.
3. It should be noted that the mean of the days set II is 3 less than the data set of I.
How to calculate the mean of the data set?1. From the information, the value of the second data set is obtained by subtracting 3 from the corresponding value of the first data set. In order to calculate the mean for each of these two data sets, this will be:
P(X > 7) = P[(X - U/SD > (7 - 5.9)/0.7]
where sd = standard deviation
= P(Z > 1.57)
= 0.058 (Checking the distribution table)
2. The standard deviation for each of these two data sets will be:
P(52.55 < x < 56.15)
= P[(52.55 - 54.2)/2.9 < x - u/sd < (56.15 - 54.2)/2.9]
= P(-0.57 < z < 0.67)
= 0.749 - 0.284
= 0.465
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Find the domain of f(x)=x-3/7x.
All real numbers except -3
All real numbers except 0
All real numbers except 7
All real numbers except 3
Using the graphical methods [online graph calculator], the domain of (fx) = (x-3)/7x is given as All real numbers except 0. (Option B)
What is a domain in mathematics?A relation's domain and range are defined as the sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively.
Graphs may also be used to determine the domain and range of functions. The domain of a graph consists of all the input values represented on the x-axis since the domain refers to the set of potential input values. The range is the collection of potential output values represented on the y-axis.
Notice as indicated in the graph that the coordinates or ordered pairs plotted DO NOT go through the origin which is zero. Also notice that the curved lines, extend to all real numbers on the grapy to infinity.
Hence stated as a mathematical expression, the domain would be:
(-∞, 0) ∪ (0,∞)
{x|x≠0}
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Julian, an experienced motorcycle mechanic, recently decided to share his expertise by
writing and selling an ebook. After conducting some market research, Julian knows that if he
charges x dollars per download, he will sell -4x + 160 downloads of his ebook in his first
year.
The online bookstore will charge Julian 25% of the amount he charges per download. So,
Julian will learn 75% of the amount he charges per download, or 0.75x dollars, in profit.
What two prices can Julian charge per download to earn exactly $900 in profit in his first
year?
Answer:
Explanation:
We know that Julian's profit per download is 0.75x dollars. Let's start by setting up an equation for his total profit, given the number of downloads:
Total profit = (profit per download) x (number of downloads)
We also know that the number of downloads Julian will sell is given by the equation:
Number of downloads = -4x + 160
So we can substitute this expression for the number of downloads into the equation for total profit:
Total profit = (profit per download) x (-4x + 160)
Simplifying this expression:
Total profit = -3x(4x - 160)
Total profit = -12x^2 + 480x
To earn exactly $900 in profit, we set the total profit equal to 900 and solve for x:
-12x^2 + 480x = 900
Dividing both sides by -12:
x^2 - 40x + 75 = 0
We can solve this quadratic equation using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
Plugging in a = 1, b = -40, and c = 75:
x = (-(-40) ± sqrt((-40)^2 - 4(1)(75))) / 2(1)
x = (40 ± sqrt(400)) / 2
x = 20 ± 10
So the two prices Julian can charge per download to earn exactly $900 in profit in his first year are $10 and $30.
To verify, we can calculate Julian's profit for each price:
At $10 per download, Julian will sell -4(10) + 160 = 120 downloads. His profit per download is 0.75(10) = $7.50, so his total profit will be 120 x 7.50 = $900.
At $30 per download, Julian will sell -4(30) + 160 = 40 downloads. His profit per download is 0.75(30) = $22.50, so his total profit will be 40 x 22.50 = $900.
An expert witness for a paternity lawsuit testifies that the length of a pregnancy is normally distributed with a mean of 280 days and a standard deviation of 13 days. An alleged father was out of the country from 242 to 303 days before the birth of the child, so the pregnancy would have been less than 242 days or more than 303 days long if he was the father. The birth was uncomplicated, and the child needed no medical intervention. What is the probability that he was NOT the father?
1. Calculate the z-scores first, and then use those to calculate the probability. (Round your answer to four decimal places.)
2. What is the probability that he could be the father? (Round your answer to four decimal places.)
1. The z scores in the question are - 2.92 and 1.769 ,
2. The probability that he is the father = 0.0402
How to solve for the probabilityThe z score for the 242 days
= 242 - 280 / 13
= -2.92
The z score for the 303 days
= 303 - 280 / 13
= 1.769
The probability that he is not the father
p(242 < x < 303)
p-value ≈ 0.00175 and 0.961553 we would have
0.961553 - 0.00175 = 0.9598
The probability that he is the father is given as 1 - probability that he is not the father.
Hence the probability that he is the father = 1 - 0.9598 = 0.0402
What is probability?
This is the term that is used in mathematics and also in statistics to refer to the likelihood of an event occurring.
The z scores are -2.92 and 1.769 while the calculated probability is 0.0402
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Which of the following is NOT a requirement for a density curve?
The option that is NOT a requirement for a density curve is option
A. The graph is centered around 0.
What is a Density Curve?A graph that displays probability is known as a density curve. All probability are represented by 100% of the curve's area under the curve.
Note that you can alternatively state that the area is equal to 1 because 100% is a decimal, which is how we typically express probabilities. Those are some characteristics of a density curve. One particular category of density curves is the normal density curve. They are bell-shaped, symmetric, and unimodal.
Therefore, To view the distribution of a variable in a dataset, utilize density graphs. The graph is plotted across a continuous range of time. Another name for this is a kernel density plot. Histograms are modified into density charts. An idealized representation of a distribution is a density curve, and there is no centered graph at point zero.
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Which of the following is NOT a requirement for a density curve?
Choose the correct answer below.
A.
The graph is centered around 0.
B.
The curve cannot fall below the horizontal axis.
C.
The total area under the curve must equal 1.
D.
Every point on the curve must have a vertical height that is 0 or greater.
In a poll conducted before a Massachusetts city's mayoral election, 134 of 420 randomly chosen likely voters indicated that they planned to vote for the Democratic candidate.
Compute a sample statistic from these data. Report your answer with three decimal places.
The sample statistic for the proportion of the Massachusetts city residents that plan to vote for the Democratic candidate is:
p = 0.319.
What is a proportion?A proportion is a fraction of a total amount, and is given by the desired amount of the sample, that is, divided the number of successes in the sample, divided by the size of the sample.
In this problem, we want to find the sample statistic for the proportion of the Massachusetts city residents that plan to vote for the Democratic candidate, hence we need to consider that:
The number of successes on the sample is of 134, which is the number of residents that plan to vote for the Democratic candidate.The sample size is of 420.Hence the estimate for the sample statistic is given as follows:
p = 134/420 = 0.319.
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The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of 4 minutes and a standard deviation of 3 minutes.
Find the probability that it takes at least 6 minutes to find a parking space. (Round your answer to four decimal places.)
The probability that it would take 6 minutes in order to get a parking space has been calculated to be 0.2524
How to solve for the probabilityThe question requires us to find the probability that it would take at least 6 minutes in order to find the parking space
The mean u = 4 minutes
The standard deviation sd = 3 minutes
The formula that is to be used for the normal distribution that we have here would be
z = x - u / sd
where P(X < 6)
xu = 4
sd = 3
When we put in these values in the equation we would have
z = 6 - 4 / 3
= 2 / 3
z = 0.6667
we are to find P(X < 0.6667) in the standard normal table
p-value ≈ 0.747518
= P(X > = 6) = (1 - P(X < 6)
= 1 - 0.747518
= 0.2524
0.2524 is the probability it would take 6 minutes in order to find the parking space.
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7) Choose the word that is most nearly similar in meaning to the word MITIGATE. A/ Exacerbate B/ Worsen C/ Alleviate D/ Escalate in the word SPORADICAL
7) Choose the word that is most nearly similar in meaning to the word MITIGATE.
A/ Exacerbate
B/ Worsen
C/ Alleviate ✓Mitigate means to make the suffering less painful and alleviate means to make the suffering more bearable.D/ Escalate
Explain regulatory requirementsExplain regulatory requirements for continuing professional development for Certificate of Registration holders: for continuing professional development for Certificate of Registration holders:real estate
The regulatory requirements for continuing professional development for Certificate of Registration holders in real estate differ from location to location. Here is an example of what obtains in the US.
What are the regulatory requirements for continuing professional development for Certificate of Registration holders in real estate in the US?According to MCKissock Learning, the Real Estate Professional must complete the following:
It is to be noted that Continuing education classes allow you to expand your knowledge and abilities in a certain field. Local school districts, colleges, and universities provide continuing education classes to individuals in the community. Courses in anything from digital design to philosophy to visual literacy are available.
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