00:01
Rida variable x is normally distributed with mean, mu equals 10, and sigma equals 2.
00:07
We wish to use a normal distribution table to find the following probabilities, a through e.
00:12
This question is challenging your understanding normal variables or random variables that are normally distributed.
00:19
To solve, let's first review relevant information related to this distribution before proceeding.
00:24
So a z table mapped z scores onto probabilities that is a probably z greater than z not equals p .n.
00:30
Implies that p .0 is the area here in purple under the z score to the right of our z knot.
00:35
So as an example, the probability z is graded in 0, for instance, is 0 for a standard normal variable z, because the mean is 0 and we have symmetry.
00:43
This segues nicely into the two theorems we're going to be using to solve this problem.
00:48
That is the symmetry of the normal curve, and the fact that the total area under the normal curve is 1.
00:53
So because random variable x is not a standard normal but instead of just a normal, we have to convert to standard normal z scores in order to compute probabilities associated.
01:01
So for instance, they're probably x greater than x equals 0 .5, we can first compute the z score to obtain zz not equals 0.
01:08
That's by converting our z score to our x, using our sigma and standard deviation.
01:13
We have x equals z not sigma plus mu or 0 times 2 plus 10 equals 10.
01:19
And b now, probably x graded in x equals 0 .95 gives z score of 1 .65...