00:01
So here we are given details that shows that this is a binomial distribution where we have the pmf to be and choose x times p to the power x times k to the power n minus x.
00:18
So p here represents the probability of heads, which is equal to 1 over 2, and q represent the probability of kills, which is also 1 over 2.
00:34
So now using the binomial theory, we are given n to be equal to a, so for part a, which says less than 5 hertz, will be equal to the probability of x is equal to.
00:55
So less than 5, the probability of x is less than 5, which is the same as probability of x less or equal to 4.
01:03
So this will be equal to probability of x is equal to 0, plus probability of x is equal to 1, plus probability of x is equal to 1, plus probability.
01:10
Of x is equal to 2 plus probability of x is equal to 3 plus probability of x is equal to so this is 0 head 1 head 2 3 and 4 so this will be so because we have many we're going to make it a summation of the x is from 0 to 4 of our n which is 8 choose x since we are summing from 0 to 4 and our p which is 1 over 2 to the power x then we have a cure to be 1 over 2 to the power n which is 8 minus x so when we do this on our calculator you're going to get 0 .6 .63 6 .67 1 875 is our answer and we know our standard deviation will be the square root of n times b times k so this will be to the square root of, or n is 8, we have 1 over 2 times 1 over 2.
02:23
So we get square root of 8 times 0 .5 times 0 .5 and this gives us the root of 2, which is the same as 1 .41 2.
02:42
So the variance of x will be n times v times k, which is 8 times 0 .5 times 0 .5 is the same as 1 over 2.
02:56
So we get 2 as our answer.
03:02
So when we come to the part b, why it says more than 5x, so this will be the probability of x greater than 5...