00:01
In this question, we're given that 40 % of recent college graduate plan on pursuing a graduate degree.
00:08
15 recent college graduates are randomly selected.
00:12
I'm going to explain the number of recent college graduates of 15 who plan on pursuing a graduate degree.
00:19
So the number of trials is going to be 15 since there are 15 college graduates.
00:25
In each trial, we take a look at a graduate in this sample and see whether he or she plans on pursuing a graduate degree.
00:33
Now p probability of success in a single trial there is probability of a college graduate in this sample who plans on pursuing a graduate degree and that will be 40 % or 0 .4 in decimal and this holds constant because this 40 % comes from a large population.
00:52
So x follows the binomial distribution n is 15 p is 0 .4.
01:00
Probability of x equals to r where r is the number of college graduates are 15 who plan on pursuing a graduate degree that will be 15 choose r 0 .4 to power r and 1 minus 0 .4 and 0 .6 to the power of 15 minus r.
01:21
And part a want to find probability no more than 4 of the graduates plan on pursuing a graduate degree.
01:29
So we're looking at probability of x less than equals to 4.
01:35
Now if you have the calculator that can compute binomial distribution.
01:41
You should be using binom cdf.
01:47
Cdf stands for cumulative distribution function because less than equal you will use binom cdf.
01:55
Now i will just use the manual method.
01:58
So for x less than equals to four, we can split into a few mutually exclusive case.
02:03
The first case is x is equals to zero.
02:06
All.
02:07
Now all is plus and is times.
02:12
Or, so there's a plus, x equals to 1, or x equals to 2, or x equals to 3, or x equals to 4.
02:26
For x equals to 0, just sub 0 into the r.
02:36
For x equals to 1, sub 1 into the r.
02:43
For x equals to 2, sub 2 into the r.
02:51
X equals to 3, sub 3 into the r.
03:00
And for x equals to 4, sub 4 into the r...