00:01
For this question, we were told that the number of instances of a middle ear infection in the first year of life follows a poisson distribution with a mean of 2 .7 per year.
00:13
And we were asked, what is the probability of having at most two episodes? so this is the probability that x is less than equal to two.
00:23
Now the probability function for the poisson random variable is given by this formula.
00:41
We can solve this also using software such as excel.
00:44
Now, if we use excel, we start a computation with an equal sign.
00:50
We want to use the poisson distribution function, so we select that function.
00:54
We enter 2 for the first argument.
00:56
We enter the mean of 2 .7, and for the cumulative argument, we enter true to get the probability of 0 1 or 2 episodes.
01:05
We hit enter, and we get a probability of 0 .4936 approximately.
01:15
Now, i notice that there's instructions in the question to approximate the answer.
01:20
So it's not stated explicitly how to approximate, but one way to approximate the answer would be to use the normal approximation to the poisson distribution.
01:31
So using the normal approximation, the number of occurrences is approximately a normal random variable with the mean of mu, it's given in the question, and a standard deviation of the square root of mu.
01:59
We can say x is normally distributed with a mean of 2 .7, and a standard deviation of 1 .64 3 -2...