00:01
We have been told that 75 % of all students at a college still need to take another math class.
00:06
We pick five students at random.
00:08
So we have five people.
00:10
Probability of each of these needing more maths is 75%.
00:14
0 .75.
00:16
Okay, so, since we've randomly chosen these people, they can be considered to be independent trials.
00:23
So we have five independent trials, two outcomes for each.
00:27
They either need more maths or they don't.
00:29
Same probability for each person.
00:32
So this meets all of the requirements for a binomial distribution.
00:37
So for this, you could use the binomial formula.
00:41
You could use the tables in the back of your textbook, or you could use technology, like your graphical calculator.
00:47
I'm going to use excel with the binom dist function.
00:53
This function has four arguments.
00:56
They are.
00:57
Number of successes, which here means people needing more maths.
01:01
Number of trials, probability of success, and whether or not i want the cumulative probability.
01:08
So for part a, the probability, exactly two of them needs more maths.
01:13
So x equals two.
01:16
So into excel, i put 2, 5, 0 .75, and false.
01:22
I don't want cumulative.
01:24
If i were to put in true here, it would give me two or fewer, which is not quite what i want, but we'll see that in part b.
01:31
So how many decimal places? four decimal places.
01:35
So that is 0 .0 .879.
01:43
At most 2.
01:45
So x is 2 or fewer.
01:47
Now we're going to use true.
01:50
So it's 2 .5...