00:01
This problem says assume a binomial distribution with the n value of 12 and the probability of success p of 0 .6, and we want to show our answers to four decimal places.
00:10
And we're asked to find the probability that x is equal to 6, less than or equal to 6, less than 6, greater than 6, or greater than or equal to 6.
00:16
And for our first probability, we'll use binomial pdf in our calculator since we want the probability of an exact event, and that's that we have 6 successes out of the 12.
00:24
But for everything else we'll use binomial cdf because we want cumulative probabilities that were less than less than or equal to or greater than greater than equal to 6 and for binomial pdf in our calculator we have to list three values to get the probability starting with the n value and p value which in our case is 12 and 0 .6 and then we list the x value we're looking to observe in this case six successes out of the 12 and now we can evaluate to get our probability and rounding to four decimal places we get the result of 0 .17 and then 6 6.
00:58
Next we want the probability that we're less than or equal to 6 and this means we'll use binomial cdf which also starts with the n -value and p -value so that remains 12 and 0 .6 but then we list the lower bound and the upper bound that we want the probability between and if we want to be less than or equal to 6 that means 6 is included for the upper bound and the lower bound would be the lowest possibility of 12 which would be 0 and now we can again evaluate in our calculator to get the probability and rounding to four decimal places we get 0 .3348 and next we want the probability that we're less than 6 so n value 12 p value 0 .6 and this time it's less than 6 but not less than or equal to 6 that means that our upper bound would be the next lowest whole number which would be 5 and our lower bound would still be 0 and when we we evaluate here and round to four decimal places.
01:50
We get the result of 0 .1582.
01:57
And next for our next probability, we want the probability of x greater than 6...