MHB -aux.06.normal distribution to standard distribution

AI Thread Summary
The discussion focuses on converting a normal distribution to a standard distribution using z-scores. The calculations involve determining z-scores for specific values, with results showing probabilities using a z-table. The first part calculates P(.70<X) as 0.8413 and P(.70<X<.79) as 0.5328. The second part approximates a value c related to a 3% probability, resulting in c being approximately 0.65. Overall, participants confirm the calculations and emphasize the value of seeking assistance.
karush
Gold Member
MHB
Messages
3,240
Reaction score
5
so for (a) (i) I used $\frac{x-\mu}{\sigma}=z
$\dfrac{0.70-0.76}{0.06}=-1 = a $ and $\frac{0.79-0.76}{0.06}=.5 = b$
ii $P(.70<X)$ z-table for $-1$ is $0.3413$ so $0.3413 + .500 = 0.8413$
$P(.70<X<.79)$ z-table for $.5$ is $0.1915$ so $0.3413+0.1915=0.5328$
 
Last edited:
Mathematics news on Phys.org
Looks good so far! (Sun)
 
(b) (i)
View attachment 1139

(ii) z-table for $3\% \approx -1.88$

so $\frac{c-0.76}{0.06}=-1.88$ thus $c\approx 0.65 s$

my shaky attempt at this anyway(Wasntme)
 
Again, looks good! (Clapping)
 
MarkFL said:
Again, looks good! (Clapping)

well, it definitely pays to ask for help...:cool:
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Thread 'Imaginary Pythagoras'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
Back
Top