00:01
Hello students, we have given that 30 % of all the customer who enter a store will make a purchase.
00:07
So, probability p is given which is equal to 0 .30.
00:11
Then suppose that 6 customers enter the store and these customers make independent purchase decisions.
00:19
So, sample size n is equal to 6.
00:21
Now, suppose x is the random variable which is the number of 6 customers who will make the purchase and it follows the binomial distribution.
00:34
Binomial distribution with parameters n is equal to 6 and probability p is equal to 0 .30.
00:40
Then we know the probability density function of binomial is probability of x is equal to x that is equal to ncx into p raised to x into 1 minus p raised to n minus x where the range of x is from 0, 1 to up to n.
01:01
So, this is equal to 6cx into 0 .30 raised to x into 1 minus p that means 1 minus 0 .30 is 0 .70 raised to 6 minus x.
01:19
Now, we have to calculate the probability that exactly 5 customers make a purchase that means probability of x is equal to 5.
01:28
So, this is equal to 6c5 into 0 .30 raised to 5 into 0 .70 raised to 6 minus 5 and that is equal to 0 .0102...