00:01
Here we consider a binomial random variable y based on 25 trials and probability of success of 0 .4.
00:10
So this should actually be y not x, or y is the number of successes out of 25 trials.
00:20
We are first asked to find the exact probabilities of y being at most 8 and y being equal to 8, and then compare them to the corresponding probabilities estimated using the normal approximation.
00:34
So first, for the probability that y is at most 8, the probability function for a binomial random variable is given by this formula.
00:58
For the probability of y being at most 8, let's use excel to solve this.
01:03
So in excel, we start a computation with an equal sign.
01:07
We want to use the binomial distribution function.
01:10
For the number of successes, we enter 8, number of trials, 25, probability success is 0 .4.
01:17
For the cumulative argument we enter true because we want the probability of any number of successes from 0 up to 8.
01:24
We hit enter and we get a probability of about .2735.
01:38
And then for the probability that y is equal to 8 exactly, let's use the probability function.
01:45
So we have 25, use 8, times .4 to the exponent 8 times .6.
01:57
To the exponent 17.
02:01
And this comes out to .11 or .1200...