00:01
In our question, for solution of our first part, first of all, we will put our sample size, that is 20, n is equal to 20.
00:08
P is given here as 0 .40.
00:11
So for the solution of a part, where we need to find the mean and standard deviation of x.
00:23
So for finding our mean, our formula will be mean, that is n into t, which will be as 20 multiplied by, 0 .40 so that is equal to 8.
00:36
So our mean is equal to 8 and now our standard deviation deviation that is from the formula square root of n into p 1 minus p which is known as cube.
00:51
So we have our value for n into p that is mean 8 then 1 minus 0 .40 so when we compute we will get here our standard deviation as 2 .1909.
01:09
So our solution for a part answer for a part.
01:14
We are having our mean that is equal to 8 and standard devision that is 2 .1909.
01:25
So this is our solution for first part of the question.
01:29
Now coming to the next part which is part b.
01:33
So here we need to find the probability for getting x is equal to 10 so for that we'll find first probability of getting x is less than or equal to 10 that is equal to that is equal to probability of getting x is equal to 0 added by probability of getting x is equal to 1 and so on up to probability of getting x is equal to 10 all the probabilities are added in so we will use your binomial expression distribution that is 20 c 0 then p which is 0 .4 to the whole power 0 and then 1 minus 0 .4 to the whole power 20 minus 0 so we will use this formula for all the probabilities till the last which is 20 c 10 0 .4 to the whole part time 1 minus 0 .4 to the whole power 20 minus 10 so so when we compute all the probabilities, our values are for the first one that is 0 .000 0 .004.
02:39
Added by probability of getting x is equal to 2 that will be as 0 .0 .0 .49.
02:48
I'm sorry.
02:49
Next is probability for getting x is equal to 3 is 0 .01, 2 ,3 .5.
02:58
Probability for x is equal to 4, that is 0 .034.
03:03
3499 next we have probability for x is equal to 4 that is 0 .0 7465 next is 0 .12441 then we have next as 0 .16588 next is 0 .17971 then we have next 0 .15971 then we have 0 .15971 then we have 0 .159 4.
03:34
Next we have 0 .11714.
03:42
So together they are equal to 0 .8725.
03:48
So our required probability for the event x is greater to less than equal to 10 is here.
03:55
So this is our required solution for b part of the question.
03:58
Answer for b part.
04:02
Now for the c part where we need to find probability for getting x is equal to 12 i'm sorry greater than 12 we will compute all the probabilities which are greater than 12 so x is equal to 13 added by probability of x is equal to 14 up to 20 added by probability of getting x is equal to 20 so all the probabilities again we will add them and their values will be from the exponential distribution 20c 30, 0 .4 to the whole power 30, 1 minus 0 .4 to the whole power 20 minus 13 and so on...