00:01
In this problem, we have a random variable is normally distributed with mean mu equals 0 .4 and standard deviation sigma equals 0 .05.
00:09
Based on this information, we want to answer a through c below.
00:13
So, this question is challenging our understanding of how to determine the answer to a standard normal variable problem.
00:20
To answer, we have to rely on information relevant to the normal distribution.
00:24
On the left, we have information relevant to mapping z scores under parallel probabilities for standard normal distribution.
00:31
However, since our distribution is not standard normal, but simply normal, we have to make the conversion to standard normal using the conversion factor z equals x minus m u over sigma.
00:40
So with the information on the left and right, we can proceed to answer a through c.
00:43
And a, we want to answer what is the probability x is greater than 0 .5? this is equivalent to saying what is the probability z is greater than a z score 0 .5 minus 0 .0 over 0 .05 equals 2...