00:01
In this problem, it is said that 5 % of workers in the us use public transportation to get to work.
00:07
Now, 250 workers are randomly selected, and we need to find the probability that exactly 160 workers say that, yes, they use public transportation to get to work.
00:18
So if x is the random variable, which counts the number of people who say yes, then this random variable follows a binomial distribution.
00:32
Now the reason for that is that all four conditions for being a binomial distribution are satisfied.
00:38
The first condition is that the number of trials should be fixed.
00:41
So the number of trials in is in this case 250 because 250 people are asked.
00:48
So that's the number of trials.
00:49
It is fixed.
00:50
So the second condition for being a binomial distribution is that each trial should be independent.
00:55
And in this case, the trials are independent because whether one worker says that they use public transportation to get to work, this does not affect in any way or form whether the other workers use public transportation.
01:07
So all the trials are independent.
01:09
Now the third condition is that there should be exactly two outcomes, a failure and a success.
01:13
In this case, since x is the number of people who say yes, so the success is a person saying yes, and a failure is the person saying no...