00:01
So this question we're told that the species of mouse is normally distributed.
00:06
Its mass is normally distributed with a mean of 19 .1 grams and a standard deviation of 0 .17 grams.
00:16
So now what's the probability that a randomly chosen mouse has a mass of less than 18 .88 grams? well actually, before we start doing this, let's note that we can write z is x minus 19 .1 divided by 0 .17.
00:30
This is going to be normally distributed with a mean of zero and a variance of one.
00:34
So this is our standard normal variable, and it's going to be easy to look up its quantiles and its cumulative function.
00:42
So we're going to work in terms of this z.
00:46
So the probability that x is less than 18 .88 grams is the probability that z is less than 18 .88 minus 19 .1.
00:58
And then that divided by 0 .17 to give us minus 1 .2941.
01:06
And now this is something we can look up in a table, or we can use a computer to do it.
01:11
I'm going to do that.
01:12
I'm going to use r.
01:14
And in r, we just have to write p norm minus 1 .2941.
01:21
So let's do that.
01:23
P norm minus 1 .2941.
01:30
And that gives us 0 .097, 8 to 4 decimal places.
01:46
Part b, what's the probability it has a mass of more than 19 .29 grams? so the probability that x is greater than 19 .29 is the probability that z is greater than 19 .29 minus 19 .1.
02:03
And then that divided by 0 .17 to give us 1 .1176.
02:13
So this is going to be 1 minus the probability that z is less than 1 .1176.
02:21
And then we can look that up in a table or use r.
02:24
So i'm going to use r...