00:01
In your question, we're told that x stands for the temperature on a random day in february in any year.
00:06
It says assume that x follows a normal distribution.
00:10
That's what this means here that i've written out.
00:12
X is approximately normal with a mean of negative 5 .3 and a standard deviation of 2 .4.
00:20
In part a of your question, we want to find 15 % of the days in february are colder than which temperature.
00:26
What i like to do is draw the normal distribution so that we can illustrate what we're looking for.
00:34
We know our mean is at negative 5 .3.
00:37
And you're looking for a temperature, which i'll call x, such that 15 % of the days are colder.
00:46
So this region represents 15%.
00:48
Now, more than likely, you're going to need technology for this question because 15 % is not a value that you can find exactly on a z table.
00:59
So the program we're going to use here is called inverse norm i'm using a ti -84 calculator and that's found under the second distribution key okay, so what we type in for inverse norm the first number we type in is the percent from the left of the distribution for us that's 15 % so that's 0 .15 as a decimal then you would type in your mean which is a negative 5 .3 and your standard deviation last at 2 .4 okay, let me type that in, and that comes in at a temperature of negative 7 .787 degrees celsius...