00:01
Hello student let's take a look at this question.
00:04
In this question we are given that p value is equal to 0 .47.
00:10
Sample size n is equal to 30.
00:13
So we can find the value of q.
00:16
Q is nothing but 1 minus p.
00:18
That is the failure rate whereas p is the success rate.
00:21
So q is equal to 1 minus 0 .47 which is 0 .53.
00:27
So let here the x represent the number of that x represent the number of repeat the number of repeat repeat repeat offenders so first we clearly observe that x follows binomial distribution with parameters n is equal to 30 and p is equal to 0 .47 so coming to the first part of the question we can calculate the probability that x is equal to 14 that is the number of repeated offenders of 14 is equal to we are going to use the formula ncr p power r q power n minus r so let's substitute the values in this so p of x is equal to 14 is equal to n value is 30 so 30 c 14 times with 0 .47 power 14 0 .53 power 30 minus 14 is 16 so on calculating this we get the required probability p of x equal to 14 is equal to 0 .147.
01:37
So this is the required probability for the first part of the question.
01:41
Now next we have probability that x is equal at most 15.
01:47
At most 15 is represented as t of x less than or equal to 15.
01:52
So this is equal to summation from x is equal to 0 to 15, 30 c x 0 .47 power x and 0 .53 power 30 minus x.
02:04
So on substituted, the values from 0 to 15 and adding them all, we get the required value as p of at most 15 is 0 .6963.
02:15
So this is the required solution for the second part of the question.
02:19
Now next we have pf at least 12...