Normal Distribution - Probability - Functions to find μ, Z,

[MistaMista]

Hello! I have trouble finding the mean and probabilty when only the standard deviation is given.
I have the correct answer, look below questions.

I think NORM.S.DIST might be the correct formula, but I cant figure out HOW to use this to get the solution.


QUESTION 1) A Top-load washers at a laundromat washes clothes with a standard deviation of 20 seconds.

Without knowing the mean, whats the probablity the machine will finish the washing within +/- 20 seconds of the mean?

SOLUTION: 0.6826

QUESTION 2) what is the probability the machine will finish the washing before a time of 10 seconds plus the mean? (Still without knowing the mean)

SOLUTION: 0.69

 

[shg]

	A​	B​
1​	0.682689​	A1: =NORM.S.DIST(20/20, TRUE) - NORM.S.DIST(-20/20, TRUE)
2​	0.691462​	A2: =NORM.S.DIST(10/20, TRUE)

 

[MistaMista]

Thank you so much shg! Do you know any sites who explains this or shows the formula is this were to be done manually? Why we are dividing with the standard deviation

	A​	B​
1​	0.682689​	A1: =NORM.S.DIST(20/20, TRUE) - NORM.S.DIST(-20/20, TRUE)
2​	0.691462​	A2: =NORM.S.DIST(10/20, TRUE)

 

[shg]

Wikipedia has excellent articles on Z scores and the normal distribution.

There is only one shape for a parabola; you can move and scale any parabola in x and y to look exactly like y = x^2. Not so for third-order polynomials; they can have a hump or not, and you can't change that by moving and scaling.

Like a parabola, there is only one normal distribution. Changing the mean moves it left or right (which here you don't care about, so zero is as good an assumption as any other), and changing deviation scales it in x. So if you use a mean of zero and the z score (x divided by the deviation) instead of x, you have a normal standard distribution.