00:01
We first consider a random variable x that is normally distributed with a standard deviation of 15.
00:06
And we're told that the probability that x is at most 50 is 0 .9904.
00:13
And we were asked to find the mean of this variable.
00:18
One way to approach this is to use the standard normal distribution.
00:22
So we first standardize the random variable according to this formula.
00:26
And so if we standardize we have the probability that z is at most 50 minus the mean over the standard deviation of 15 is equal to 0 .9904.
00:52
We can also go to the standard normal table and see what z -score corresponds to a cumulative probability of 0 .9904.
01:05
So let's leave this blank, go to the standard normal table, look for the cell that has a cumulative probability of 0 .9904 in it.
01:15
That's the cell, that's a z -score of 2 .34.
01:24
So looking at these two equations, they tell us that 50 minus the mean over 15 must be equal to 2 .34.
01:42
And solving for mu, we get 14 .9.
01:46
So the mean for that distribution is 14 .9.
01:52
And then there's a second question...