An educated person should hear Mozart, read Shakespeare, and see the equation of the normal distribution.

Some of you agreed that you are making asymptotic progress on your homework – getting closer and closer but never finishing.

Movie price example

Finishing off the movie price example

Microwave oven example, part a

The sketch for the microwave oven example part a

Part b …

The sketches for part b. We had to cut a big slice of pie (z<-0.36) and then cut the tip off of that (z<-2.14) to be left with the exact slice we want.

This is an easy one. The probability that x is greater than the mean is always and only one-half, for a symmetrical probability distribution like the normal.

After a little “word problem translation”, part d turned out to be another way of asking the question from part a.

The “Lake Osoyoos” problem. If we want to go on using the table from the left-hand page (the one with the tail areas), we need to do some manipulations …

… like so. We find the left-side (negative z) tail, flip it to the right side (positive z) using the symmetry of the distribution, and then we subtract that area from one (the total area under the curve) to be left with the stuff we want. Or, we could just use the table on the right-hand page (which gives “bulk” areas instead of tails) … but it’s good to know how to find these areas from any version of the table.

Lake Osoyoos, part c

The sketch for part c.