00:01
In a survey of health workers, 25 % stated that they expect to be promoted after three years of service.
00:10
If this percentage holds for the entire population and a sample of nine health workers drawn from this population, determine the probability that the number expecting a promotion within three years of service are six, at least four, no more than five, between six and nine inclusive.
00:30
For a probability of x equals six, we can use our binomial probability.
00:33
So 9 combination 6 times 0 .25 to the 6 power times 0 .75 to the third power.
00:41
And that's going to give us 0 .0087.
00:49
For the probability of at least 4, no more than 5, and between 6 and 9, we can continue on.
00:59
So the probability, using our probability, so the probability that x is at least 4, means that we're going to want to take, in my case, i'm going to take 1 minus the probability of 0 plus probability of 1 plus the probability of 2 plus the probability of 3, because that would be faster than 4, 5, 6, 7, 8, 9.
01:27
So you can see here that i've listed out those probabilities.
01:31
Now i'm going to add them together.
01:33
That's 0 .8343.
01:40
So again, the probability that x is greater than or equal to 4 is going to be 1 minus this probability.
01:49
And when i subtract that from 1, i get my probability of 0 .1657.
01:57
Next we're going to do the probability that it's no more than 5.
02:02
So that would be x is less than or equal to 5...