00:01
In this question we are told that vocabulary scores for a certain test for seventh grade students, let's call these scores random variable x, are normally distributed with a mean of 6 .8 and a standard deviation of 1 .6.
00:20
So part a we are asked to write the event.
00:24
The student chosen has a score of 6 .8 or lower in terms of x.
00:33
So this is some instantiation of the random variable x, and it says 6 .8 or lower means less than or equal to 6 .8.
00:51
And then for part b, we are asked to find the probability of an event, which represents the student's chosen score has a score of, the chosen student has a score of 6 .8 or lower.
01:02
So we write that like this, probability that x is less than or equal to 6 .8, and we're asked to find this probability.
01:12
So if this distribution here represents our normal distribution for these vocabulary scores, the mean of 6 .8 is right in the center of the distribution, and the standard deviation is 1 .6.
01:29
The probability that x is less than or equal to 6 .8 is equal to the area under the curve and to the left of 6 .8.
01:41
Now 6 .8 also happens to be the mean of this distribution...