"I understood that naturally occurring phenomenon such a weight of all individuals form a bell curved normal distribution, with more frequency applied to the center. but I'm confused with the arithmetic operators used to derive the Z-score of the standard normal distribution. Say, I found the mean weight of a population to around 60kg and to convert to standard normal distribution I first subtracted the individual weight/random measure by the mean i.e. with 60kg but then moving on why are we dividing it by (sigma) the standard deviation to find distance of how far the data point is away from the mean. Why did we use the arithmetic operation of division and why divide with sigma (the standard deviation) to find the Z-score? Can someone help out to conceptualize the idea."

What is the range of the function ${\displaystyle y=x^2}$?

The domain and range of $y=\sin <!--\; \; -->x$ is
A)$R,[0,\mathrm{\infty <!--\; \infty \; -->}]$
B)$R,[-<!--\; -\; -->1,1]$
C)$R,[-<!--\; -\; -->\mathrm{\infty <!--\; \infty \; -->},\mathrm{\infty <!--\; \infty \; -->}]$
D)$R,[1,\mathrm{\infty <!--\; \infty \; -->}]$

Mean of the squares of the deviations from mean is called the:
Variance
Standard deviation
Quartile deviation
Mode

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Find the range of ${\displaystyle \frac{x^2}{1-x^2}}$

State the main limitations of statistics.

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In most cases,_____variables are not considered to be equal unless they are exactly the same.

A local newspaper in a large city wants to assess support for the construction of a highway bypass around the central business district to reduce downtown traffic. They survey a random sample of 1152 residents and find that 543 of them support the bypass. Construct and interpret a 95% confidence interval to estimate the proportion of residents who support construction of the bypass.

$3+3x3-3+3=?$What is the right answer and how?

Define lateral displacement.