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Recent questions in Descriptive Statistics

hard12bb30crg 2022-05-15 Answered

$X \sim N (15, 4)$
Find P( X > 18.7 | X > 11.7 ).
Attempt: Rewrite as P ( x > 18.7) - P( x > 11.7)
Using the phi function
$ϕ (1.85) - ϕ (- 1.65) = (0.9678) - (0.0495) = 0.9183$
Where did I go wrong?

Spencer Lutz 2022-05-13 Answered

I'm new here and was hoping you guys could help me with a statistics problem that I don't quite understand. I'm not sure if it's proper etiquette to ask for help on a specific homework problem here, so I apologize if this question is out of line.

Here is the problem:
Suppose a variable of a population has mean 5 and standard deviation 11. For samples of size 121, find $c$ so that $P (X > 2 c) = 0.3300$ .

britesoulusjhq 2022-05-13 Answered

Mentioned that the mode of negative binomial distribution can be found by: t = 1 + ((r-1)/p) where t is some number, r is the number of successes and p is the probability of success If t is an integer, there will be 2 modes at t and t-1 If t is not an integer, the integer part of t is the mode.
This is what I have worked on so far: ((r-1)/p) is the expected number of attempts to achieve all required successes excluding the final success The expected number of attempts + the definite final success = the total number of expected attempts.The total number of expected attempts is the mode.
Why could there be two modes of t-1 and t?
$P (X = x) = ((x - 1) c h o o s e (r - 1)) (p^{r}) (q^{(x - r)})$
$((t - 2) c h o o s e (r - 1)) (p^{r}) (q^{(t - r - 1)}) = ((t - 1) c h o o s e (r - 1)) (p^{r}) (q^{(t - r)})$
$((t - 2) c h o o s e (r - 1)) (q^{- 1}) = ((t - 1) c h o o s e (r - 1))$
$((t - 2) (t - 3) . . . (t - r)) / (r - 1)! x (q^{- 1}) = ((t - 1) (t - 2) . . . (t - r + 1)) / (r - 1)!$
$(t - r) / q = t - 1$ [I am stuck here]

Merati4tmjn 2022-05-09 Answered

I have a set of 1000 data points. I would like to estimate their mean using a confidence interval. I read somewhere that if the sample size, $n$ , is bigger than 30 you should use a t-score, and else use a z-score.
Is that true?

Matilda Webb 2022-05-09 Answered

The probability density function of the random variable $X$ is defined by
$f (x) = {\begin{cases} 4 (x - x^{3}), & 0 \leq x \leq 1 \\ 0, & elsewhere \end{cases}$
What is the probability that three independent observations from the distribution of $X$ are all less than the mode of $X$ ?
This is a question I got incorrect. I have very little experience with mode and I understand that it's the value of the random variable with the highest probability. The solution for finding the mode is as follows:
The max point occurs when $f^{'} (x) = 0$
$f^{'} (x) = 4 - 12 x^{2} = 0$
$x = \sqrt{\frac{1}{3}}$
This is the max point or mode because $f^{″} (x)$ is a negative number.

Ashley Fritz 2022-05-09 Answered

How do you define a variable and write an algebraic expression for the phrase: 3 increased by a number?

affizupdaftf3opg 2022-05-08 Answered

How can I calculate the mode in a grouped frequency distribution when the largest frequency occurs in two or more classes?

Deshawn Cabrera 2022-05-08 Answered

My main goal is to calculate the sampling variance. But I will start with the standard deviation. I am doing a meta-analysis and need to calculate the variance for EACH effect size (prevalence in this case) in each study.
For example, I have 10 positive cases out of 1000 people that were tested. This gives a prevalence of 0.01 (or 1%). How do I find the standard deviation from this information?

Reese Estes 2022-05-07 Answered

What is the mean score for the 20 rolls?
A fair die is rolled twenty times. The results are shown in the bar graph. What is the mean score for the 20 rolls?

velinariojepvg 2022-05-07 Answered

The scores obtained on a Test can be normally distributed with mean $μ$ = $100$ and standard deviation $σ$ =15.What percentage of scores lie: Below 85?
Progress: used formula $\frac{𝑥 - 𝜇}{𝜎}$
Got -1 which corresponds to 0.15866 on z score table
Since it asks for scores below 85 do i minus 1 (the sum of all values) from the value i got ?

Yasmine Larson 2022-05-07 Answered

A class average for a test is 75 with a standard deviation of 6. How can I use this to calculate the percent of ata that are below the z score of $z = - 1.50$ . The possible solutions are &6.81%, 6.68%, 7.35%, 8.08%&

Peia6tvsr 2022-05-07 Answered

Carrie is performing an experiment on acids and bases, so she forms the following hypothesis: If an acidic solution is added to a basic solution, the pH of the resultant solution will decrease. What is the dependent variable in Carrie's experiment?

Dominick Blanchard 2022-05-07 Answered

A student took a math exam and scored 77. If the class exam scores were mound-shaped with a mean score of 70 and standard deviation of 16, use z-score to determine how the student placed comparing with the class average i.e. is the student's mark an outlier or not?

So my attempt: I used this equation
$n = μ + σ z$
where
1. $n$ is the data point (77)
2. $μ$ is the mean (70)
3. $σ$ is the standard deviation (16)
4. and $z$ is the $z$ -score (unknown)

To solve for the unknown:
$\begin{aligned} 77 & = 70 + 16 z \\ 7 & = 16 z \\ 0.4375 & = z \end{aligned}$
This value is equivalent to 0.6700 on the z table. I just don't know what to do with this information and what steps I would take next to figure out the question.

Karissa Sosa 2022-05-07 Answered

Suppose
where $x$ is normal with mean $μ$ and variance $σ$ . Then I see how to derive mode of $f (y)$ (distribution of $y$ ), as we need to find the value y that makes
$f^{'} (y) == 0$
However, why is mode not simply
$e^{μ}$ ?
$y$ is a monotonic function of $x$ , and so when $x$ reaches its mode, then y should also reach its mode. The mode of $x$ is its mean ( $μ$ ) hence $y$ 's mode should be
$e^{μ}$
what mistake have I made?

Caitlyn Cole 2022-05-03 Answered

Find the critical value that corresponds to a 90% confidence level.

I know that the answer is 1.645. But i tried to look it up on the Z score table, but i couldn't figure out how to read it. I did the following: 0.9+1 = 1.90.
I then look at the left side for 1.9 and on the top i search for 0.0, the number that is stated there is 0.9713. Which isnt true.
Can someone explain me please how to use the Z-table

Maeve Bowers 2022-05-03 Answered

Suppose that $X$ has the Binomial distribution with parameters $n, p$ . How can I show that if $(n + 1) p$ is integer then $X$ has two mode that is $(n + 1) p$ or $(n + 1) p - 1 ?$ ?

Taliyah Spencer 2022-05-03 Answered

Looking for some real world examples for mode in Statistics involving topics which students like say Football or Social networks. Also they need to clearly identify differences in the usefulness of mode and mean. For example which player to pick for a football match depending on scores against a particular team while playing against that team. Mean doesnt make sense here. Any thoughts ?

Bailee Ortiz 2022-05-03 Answered

Trying to find the probability $b / w$ two scores. I know mapping to $z$ -score is:
$z_{11} = (11 - 10) / 1.5 = .67$
and
$z_{14} = (14 - 10) / 1.5 = 2.67$
So,
$\bar{x} = 10, σ = 1.5.$
Would I simple subtract the two from each other? and so on the real number line it would range from 0 to 100 and that is how the distribution would be set up. So, 2.67−2=2?

On the z-table 2 is given a value of 0.9772.

My teacher likes to give things as either a proportion or a percentage so how might one be able to address the two. Like if this question was asking for the proportion of scores that fall between 11 and 14 or if the question said what's the percentage of scores that fall between 11 and 14. How might be able to address both scenarios?

Just confused on the ideas of proportion, probability, and percentage and how they are relate.

airesex2 2022-05-01 Answered

For z score, you are taking the sample value subtracting population mean and dividing it by std deviation. Is that correct so far?
Now, the "sample value" is defined by an equation. In my scenario, I have a bunch of stores that are reviewed by their customers. The customer amount varies. One store has 2 customers who give review while other store has 19 people who give reviews. For the 1st store in my example, both customers give 5/5. while the 2nd store customers, avg score given by all 19 customers is 4.
Sample value is calculated as score/customer count. So for the 1st store, it will be 5/2 while the other store will be 4/19. If I use that in z score eq. it will mean that first store is doing much better than the last store. I would like to know how to make the score "proportional""normalized""fair" etc...
Oh my many gods, I can't believe I ended like that. Thanks for pointing that out.

Magdalena Norton 2022-05-01 Answered

Without assuming that the diameters of apple pies are distributed according to the normal distributions, estimated the probability that the mean diameter is larger than 32 cm. The sample standard deviation is estimated to be 2. The sample mean is 28 and the sample size is 100.
When I used CLT (because the sample size is >30). I am getting a z score of 20? Is this correct?

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