00:01
Hello, students, we need to write here, let x be a binomial random variable with n value and probability value is given.
00:08
We need to use normal approximation to find probability random variable value is greater than 20.
00:16
So first, we need to consider x as binomial.
00:22
So basically, if i write for this, this is considered as as binomial distribution.
00:28
So basically, if i write here, n comma p we need n value is 30, comma probability value is 0 .5.
00:40
So probability of success is p, so probability of unsuccessful is 1 minus p.
00:46
So 1 minus 0 .5 is again 0 .5 if i calculate this.
00:50
1 minus 0 .5 is again 0 .5.
00:57
Now let us come to other part.
00:59
So if i write for this, mean, value will come out as mean value is basically mu is equals to np so n is 30 np is 0 .5 so basically this is 15 and now let us talk about what is our standard deviation sigma value standard deviation sigma will come out as under root of np multiplied by 1 minus np so obviously under of npq so this is under root of 30 multiply by 0 .5 multiplied by 0 .5 so if i calculate this this will come out as 2 point so basically this is 30 multiplied by 0 .25 this will come out as under root of so this is let's say 2 .5 multiplied by 3 which is 7 .5 and this will come out as 2 .74 so as sample size is greater now we need to consider this as normal distribution.
02:12
So in the normal distribution we all know all the random variables are distributed amongst bell shaped curve quickly overview.
02:21
We can see here this is like this and this is minus z plus z probability of z, sum of all probabilities equivalent to total area right here which is one.
02:33
And left -hand side area is 0 .5, right -inside area is 0 .5.
02:37
This is x is equal to mu.
02:39
It means z is equal to 0.
02:41
We need probability random variable value is greater than 20.
02:46
So for that, what we need? we need our z score value in that case, which is x minus mu, divided by sigma.
02:54
Mu is mean and sigma is standard deviation.
02:56
If i write here, so x is 20 minus mu...