00:01
Let x follows binomial distribution n, p where n is equal to 7 and p is 0 .5.
00:10
So binomial distribution formula is p of x is equal to x is equal to ncx p raise to x 1 minus p raise to n minus x.
00:22
Part a, the mean of x is calculated using the product of n and p.
00:28
On substituting the values 7 multiplied with 0 .5 which is 3 .5 that is the mean.
00:38
Part b, standard deviation of x is calculated using the formula square root of np multiplied with 1 minus p.
00:52
So square root of 7 multiplied with 0 .5 multiplied with 1 minus 0 .5.
00:58
On simplifying we will be getting 1 .3229 which is the standard deviation of x.
01:07
And part c, p of x greater than 3 .5.
01:12
This can be written as p of x greater than or equal to 4.
01:17
Since x is discrete, it can take values 0, 1, 2, 3, 4, 5, 6 and 7 only.
01:28
So p of x greater than or equal to 4 means p of x is equal to 4, 5, 6 and 7.
01:45
Applying the binomial distribution formula 7c4 multiplied with 0 .5 raise to 4 multiplied with 0 .5 raise to 3 plus 7c5 0 .5 raise to 7 plus 7c6 multiplied with 0 .5 raise to 7 plus 7c7 multiplied with 0 .5 raise to 7...