# Announcement

Frédéric Boileau shared on facebook group a math323 notes taken by Ryan Ordille in Winter 2012 semester. I wish that I knew this note existed before I start my own from scratch.

Since the quality of Ryan’s notes is so good, it’s better to improve that notes rather than keep making a new one.

That said, this serie of notes will be continued in a different way – I’ll only take down the notes that are missing on Ryan’s version.

# Supplemental Notes

Today’s notes is found on Ryan’s page 33.

## Example (Similar Problem)

A dispensing machine dispenses milk into 1 litre containers, such that the amount dispensed has an approximate Normal Distribution with standard deviation $.1$ and mean $\mu$, that can be adjusted. What should the mean be adjusted to so that the proportion of overflow is 0.25?

## Solution

Let $X$ be the amount dispensed and let $\mu$ be the mean amount dispensed. Here $X\sim N(\mu,(.1)^2)$

Want $\mu$: $P(X\geq 1) = 0.25$. Reduce to a standard normal, want $\mu$ : $P( \frac {X-\mu} {.1} > \frac {1-\mu} {.1}) = 0.25$

[Complete this as for the battery problem except $\mu$ is the unknown]. Answer is $\mu = 0.804$

Then comes the Transformation of random variable, this is on section 18.3 of Ryan’s, page 38.