-aux.06.normal distribution to standard distribution

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Discussion Overview

The discussion revolves around the conversion of a normal distribution to a standard distribution, specifically addressing calculations involving z-scores and probabilities related to a given dataset. The context includes homework-related problems and mathematical reasoning.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant calculates z-scores for values 0.70 and 0.79 using the formula $\frac{x-\mu}{\sigma}$ and provides corresponding probabilities from the z-table.
  • Another participant confirms the calculations and expresses approval.
  • A different participant attempts to find a value 'c' corresponding to a z-score of approximately -1.88, indicating uncertainty in their approach.
  • Further confirmations of the previous calculations are provided by other participants, suggesting a supportive environment for sharing solutions.

Areas of Agreement / Disagreement

Participants generally agree on the calculations presented, but there is some uncertainty expressed by one participant regarding their own calculations.

Contextual Notes

Some calculations depend on the accuracy of the z-table values used, and there may be assumptions regarding the normality of the distribution that are not explicitly stated.

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 $0.3413+0.1915=0.5328$
 
Last edited:
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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:
 

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