MHB -aux.06.normal distribution to standard distribution

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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
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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 $0.3413+0.1915=0.5328$
 
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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:
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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