00:01
This question we have given 10 % of people are left -handed.
00:10
Also it is given that 12 people are selected at random.
00:20
So let us take you be the left -handed people that is equal to 0 .1 as it is given as 10 % therefore, p is equal to right -handed people is equal to 1 minus q that is equal to 1 minus 0 .1 that is equal to 0 .9.
00:41
Now we will use formula distribution formula that is given us p of x is equal to ncx times p r r r to the power x times p rest to the power n minus x.
00:58
Now in part a, we have to find the mean and the standard deviation.
01:03
Of a number of right -handed people in a group.
01:07
Being of binomial distribution can be given as mu of x is equal to n times p.
01:21
And the standard deviation can be given as sigma of x is equal to under root of n times p, multiplied with 1 minus p.
01:33
Therefore, mean of right -handed people is equal to 12 multiplied with 0 .9, which is equal to 10 .8.
01:47
And standard deviation of right -hand -hand people is equal to under root of 12 multiplied with 0 .9, multiplied with 1 minus 0 .9.
01:57
That is equal to 1 .04.
02:00
In part b, we have to find the probability that the selected people, are not all right hand.
02:08
So probability of not all right -handed is equal to one minus probability of all right -handed people.
02:17
That is equal to one minus probability of x is equals to 12.
02:22
That is equals to 1 minus 12 12 multiplied with 0 .9 x to the part 12.
02:33
Here we have used formula 1.
02:36
On further simplifying we get it as 0 .718.
02:42
Now in part c we have to find the probability that there are no more than 11 rites...