How do you calculate a z-score?

Alonzo Odom
2022-07-23
Answered

How do you calculate a z-score?

You can still ask an expert for help

ri1men4dp

Answered 2022-07-24
Author has **14** answers

$z=\frac{x-\overline{x}}{\sigma}$

Where -

$z$ is standard normal variate

$x$ is an observation

$\overline{x}$ is mean

Where -

$z$ is standard normal variate

$x$ is an observation

$\overline{x}$ is mean

asked 2022-05-01

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?

When I used CLT (because the sample size is >30). I am getting a z score of 20? Is this correct?

asked 2022-07-09

According to the definition I read, it came to my notice that the number with highest frequency has to be a mode for a given data set, but then what if I have all the numbers as distinct... In that scenario we won't have a particular number having a frequency more than other elements in the data set... Now if I consider a case when we have 2 numbers in a dataset with same max number of occurrences like:

$2,3,4,5,3,2$

Here 2, 3 both happen to have same maximum frequency and thus we say there are 2 modes... The above is stated similar in case we have 3 modes or multi modes ... So if there are all distinct numbers then we would have each number having the same maximum frequency as 1 ..so we can say all the numbers are modes...for that dataset...But then I have seen on some websites claiming that such data sets have "NO MODE".

$2,3,4,5,3,2$

Here 2, 3 both happen to have same maximum frequency and thus we say there are 2 modes... The above is stated similar in case we have 3 modes or multi modes ... So if there are all distinct numbers then we would have each number having the same maximum frequency as 1 ..so we can say all the numbers are modes...for that dataset...But then I have seen on some websites claiming that such data sets have "NO MODE".

asked 2022-06-17

What is an independent variable in chemistry?

asked 2022-05-28

Consider a "discrete" random variable $X$. A mode of $X$ is just a maximizer of $P(X=x)$. This is obviously useful, and we can easily see that a mode is a "most likely" value for $X$.

If, instead, we have a "continuous" real-valued random variable $X$ with a PDF ${f}_{X}$, I think we usually define a mode of $X$ to be a maximizer of ${f}_{X}$. I have two questions:

1. How can we interpret the mode of a continuous random variable? In other words, why is the mode of a continuous random variable useful to probability theory?

2. Is there a more general definition of mode, removing the assumptions above that $X$ is real-valued and has a PDF?

If, instead, we have a "continuous" real-valued random variable $X$ with a PDF ${f}_{X}$, I think we usually define a mode of $X$ to be a maximizer of ${f}_{X}$. I have two questions:

1. How can we interpret the mode of a continuous random variable? In other words, why is the mode of a continuous random variable useful to probability theory?

2. Is there a more general definition of mode, removing the assumptions above that $X$ is real-valued and has a PDF?

asked 2022-06-10

Find the mode, we need to find the value of $x$ for which ${f}^{\prime}(x)=0$ and ${f}^{\u2033}(x)<0$. After applying derivative to the pdf, how do we proceed?

asked 2022-05-09

The probability density function of the random variable $X$ is defined by

$f(x)=\{\begin{array}{ll}4(x-{x}^{3}),& 0\le x\le 1\\ 0,& \text{elsewhere}\end{array}$

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 ${f}^{\prime}(x)=0$

${f}^{\prime}(x)=4-12{x}^{2}=0$

$x=\sqrt{\frac{1}{3}}$

This is the max point or mode because ${f}^{\u2033}(x)$ is a negative number.

$f(x)=\{\begin{array}{ll}4(x-{x}^{3}),& 0\le x\le 1\\ 0,& \text{elsewhere}\end{array}$

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 ${f}^{\prime}(x)=0$

${f}^{\prime}(x)=4-12{x}^{2}=0$

$x=\sqrt{\frac{1}{3}}$

This is the max point or mode because ${f}^{\u2033}(x)$ is a negative number.

asked 2022-07-09

Is age a discrete or continuous variable? Why?