Math 323 - Class 21

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.

Link to the notes: https://github.com/ryanordille/m323w12

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.