00:01
For this problem, we are told that the lengths of a certain brand of pencil are normally distributed.
00:08
We're told that the mean is 6 inches and the standard deviation sigma is 0 .5 inches, and we want to find the probability that a randomly chosen pencil is between 5 .5 and 6 .25 inches.
00:24
So let's let x be the random variable for this distribution, the length of a randomly selected pencil, then we're interested in this probability x is between 5 .5 and 6 .25.
00:38
Now we know x is normally distributed, so let's draw a normal distribution here.
00:43
The mean is here in the middle, 6, and we want all the area from 5 .5, which is around here, up to 6 .25, which is around here.
00:53
So we're interested in computing this area.
00:56
I'm now shading in red, so that's equal to this probability.
01:03
And this is a cumulative probability of a normally distributed random variable, so we can use the cumulative function for normal distributions to work it out.
01:14
I'm going to use a ti -84 for that...