00:01
For this question, we are told that the height of giraffes is normally distributed with a mean of 18 feet and a standard deviation of 0 .8 feet.
00:08
And we are asked to express the distribution of x in the standard notation.
00:13
So here we can say x is normally distributed.
00:17
The first argument, and this is the mean, which is 18.
00:22
And the second argument is the standard deviation, which is 0 .8.
00:28
Now i just point something out.
00:29
I'm using the mean and the standard deviation, but some courses have a convention where they use the mean and the variance instead.
00:38
So if your course uses this convention, then you'd have to take this value and square it, so you'd get a variance of 0 .64.
00:49
So it's either going to be 0 .8 or 0 .64, depending on whether or not the convention in your course uses sigma or sigma squared.
01:02
For b, we are asked for the median giraffe height.
01:06
So let's say this is the normal distribution representing the giraffe height.
01:09
So we have a mean of 18 feet exactly in the center.
01:11
The normal distribution is bell -shaped and perfectly symmetrical about the mean.
01:17
By definition, the median is the value of the random variable such that 50 % of the distribution is smaller than it.
01:25
Since the normal distribution is symmetrical about the mean, for any normal random variable, the median is equal to the mean, and this is 18.
01:47
18 feet.
01:50
Then for c, we are asked for the z score for a giraffe that is 21 feet tall.
01:55
We calculate the standardized scores according to this formula.
02:04
So for 21 feet, we have 21 minus the mean of 18, divided by the standard deviation of 0 .8, and we get 3 .75.
02:24
For part d, we are asked for the probability that a randomly selected draft will be shorter than 18 feet tall.
02:30
It says the probability of x is less than 18, or not 18 feet tall, 20 feet tall.
02:38
Now if we standardize this using this formula, we can equate this to the probability that z is less than 2 .5.
02:53
And now we can look up z equals 2 .5 in a standard normal table, or corresponds to a cumulative probability of 0 .9938.
03:07
So the probability of a giraffe being less than 20 feet tall is 0 .9938...