00:01
So in this question, it is given that x is normally distributed with the mean of 500 and a variance of 300 squared.
00:14
So x here represents the amount of loss in a year.
00:17
So for our part a, we have to calculate the probability that you would leave and vegas having lost no more than $100.
00:29
So you have the probability of x less than or equal to 100.
00:32
And this will be equal to the probability of x minus mun over sigma.
00:38
So this is less or equal to we have 100 minus 500 divided by 300.
00:47
And by the central limit here, this is equal to z.
00:50
So you have z less or equal to negative 4 over 3.
00:56
Reading this from the standard number, we get 0 .0 .9 -1 -2 .1.
01:03
When we come to the path b, you have to find for the probability that you will leave vegas, having lost more than $200.
01:17
So this implies having probability of z greater than 200 minus 500 over 300.
01:29
And this will be equal to probability of z greater than negative one.
01:37
This will be equal to 0 .844.
01:47
When you come to the path c, you have to find the probability that you live vegas, having more money than you lived with, which is probability of x less than, probability of x less than zero...