Another question, the average daily high temperature in June in LA is

77 degrees Fahrenheit, with a standard deviation of five degrees Fahrenheit.

Suppose that temperatures in June closely follow a normal distribution.

How cold are the coldest 20% of the days during June in LA?

We are told that the distribution is nearly normal, with

mean 77 degrees Fahrenheit, and standard deviation five degrees Fahrenheit.

So we can draw our curve, and we also mark the coldest 20%

of the day, so that's going at the lower end of our distribution.

So the shaded area here is .20.

This time we don't know our cutoff value.

That's the number that we're trying to get to.

So in order to do that, we need to first

figure out which standardized score, or Z score this corresponds to.

We can do that using r, and in for that we're going

to use the other function that we learned about, the qnorm function.

Where the first input is the percentile, the

second input is the mean, and the third

input is the standard deviation, and that gives us 72.79.

Meaning that the coldest 20% of the days during June in LA, are colder

than 72, 72.79 degrees Fahrenheit.

Another approach would be to do this by hand.

Once again, let's draw our curve. Let's mark our percentile.

And then what we want to do is we want

to figure out, using the table, what Z-score the 0.2 corresponds to.

So we're looking in the table and we're going to

look in the center to get as close to .2

as possible and it appears that the closest we can

get is going to be somewhere between .1977 and .2005.

Well how do we choose between these two?

Let's go with the closest, so .2005. Which gives us

a Z score of negative 0.84.

We know that this value can also be calculated as the unknown observation,

minus the mean 77 divided by the standard deviation of 5, and if

we solve for X here, multiply on both sides by 5, and adding the 77, we

once again get to roughly the same answer, 72.8 degrees Fahrenheit.