00:01
In this question we are given that x is a binomial random variable, n is 100, p is 0 .2.
00:09
So q is the probability of failure in a single trial, that will be 1 minus p and that will be 1 minus 0 .2 and that is 0 .8.
00:19
Now n equals to 100 is greater than 50, n times p which is 100 times 0 .2 is 20 which is greater than 5, nq is 100 times 0 .8 and that is 80 which is greater than 5.
00:37
So this criteria shows that we can use the normal distribution to approximate the binomial distribution.
00:45
So let's find npq first.
00:48
Npq is 100 times 0 .2 times 0 .8 and that is 16 or 4 square.
00:56
So x can be following the normal distribution now, the mean is np which is 20, variance is npq which is 4 square.
01:12
Now normal distribution is continuous, binomial is discrete.
01:16
So now we have to use continuity correction when we find the probability.
01:21
So we want to find probability x is greater than or equal to 24...