00:01
For this problem, i'll regularly be using that the, or the fact that the probability of x less than or equal to some, i'll say less than or equal to some big x value can be calculated by taking the probability that a z score is less than or equal to the big x value minus the mean value of x divided by the standard deviation of x.
00:28
That being said, for part a, we are looking for the probability of, let me just double check the exact one here, so that is probability of x less than or equal to 35 .36, which is going to be equal to the probability of z less than or equal to 35 .36 minus the mean value 35 .07 divided by the standard deviation, 4.
01:02
So that's going to be equal to the probability of z less than or equal to 0 .0725.
01:11
You can find that using a table of values or using excel, something like that.
01:17
We should find that the result is equal to about 0 .5 to 889.
01:22
For part b, looking for the probability that x is in between 30 .07 and 40 .07, we can find that by taking the probability that x is less than 40 .07, subtracting off the probability that x is less than 30 .07.
01:47
When we convert that to an expression in terms of z scores, it's going to be equal to the probability that z is less than positive 1 .25 minus the probability that z is less than negative 1 .25.
02:03
And i realized i missed a zero there...